The former Watford boss, who was sacked by the Vicarage Road club last month, is apparently in the frame to take up the reins on a short-term basis and replace Italian Conte.
According to the Times, Silva is much admired by Marina Granovskaia, the club’s influential director, and is seen as a man who could life the spirits in the Stamford Bridge dressing room.
With candidates few and far between until the summer, the 40-year-old Portuguese looks to be in prime position for the role with Guus Hiddink considered another option and former Barcelona manager Luis Enrique potentially lined up.
The Dutch international moved to Anfield for £75 million (85m euros, $104m) in January, but has been on the winning side in just one of his four outings for Liverpool since.
Van Dijk got off to a dream start as he scored the winner to edge a Merseyside derby against Everton on debut.
However, hopes he would provide an instant fix to the holes in Jurgen Klopp’s defence were shattered in back-to-back shock defeats to Swansea and West Brom.
“I know because I made such a big step right now, for a lot of money, everything is going to be analysed,” said Van Dijk.
“No one is going to look at the good things that you do. Everybody is going to watch the bad things and that is how it is. But I will discuss it with the people who want to make me better, who can make me better, that is the manager and the players around me.”
Yet, there were signs of why Liverpool waited to get their man in January after an initial move for Van Dijk stalled last summer in last weekend’s 2-2 draw with top-four rivals Tottenham Hotspur.
Van Dijk largely kept the Premier League’s top scorer Harry Kane quiet until a frantic finale in which Spurs were awarded two controversial penalties – the second of which for a foul by Van Dijk on Erik Lamela in virtually the last action of the game.
“No one will talk about my performance in general. We defended very well, had two penalties against us with a lot of question marks around them, but no one is going to talk about that,” added Van Dijk.
“But I know that as a team we did very well against one of the best strikers in Europe.”
Both teams are in need of the points at different ends of the table. Third-placed Liverpool can gain more ground in the race for a Champions League place, whilst Southampton are still precariously positioned just two points above the relegation zone despite a first league win since November last week at West Brom.
However, Van Dijk insists he will have no sympathy for his former employers on Sunday.
“I made the decision, I have enjoyed every bit of it and I am very grateful for everything that they did for me. I have moved on, they have moved on.
“I know they are struggling and we need to win. I am going there with only one mindset and that is to win.
“Obviously it will be nice to see the players I have played with and the friends I have there but, for me, it is going to be about one thing only and that is to win the game.”
Liverpool return to the European stage on Wednesday when they travel to Porto for the first leg of their Champions League last 16 tie, but Klopp, who has rotated his side more than any other manager in the Premier League this season, struck down suggestions his team selection would be affected by preparations for the trip to Portugal.
“I have a few experiences with European football and I never thought about the European game the week after,” said the German.
“The main focus is always the next game, in this case Southampton. You cannot and we will not think about the Champions League game.”
Club-record signing Aubameyang shone on his Gunners debut last weekend, scoring in a 5-1 victory over Everton.
The Gabon international has taken the number 14 shirt at Arsenal previously worn by Henry – the club’s all-time leading goalscorer.
Having joined the club from Borussia Dortmund on transfer deadline day, Aubameyang compared his style to Henry and said the Frenchman is “an example” to strikers.
Ahead of Arsenal’s north London derby against Tottenham at Wembley on Saturday, Wenger urged caution over likening the pair – although he was pleased Aubameyang has set such lofty aspirations.
“It is an ambitious statement but it is a good one,” he said.
“(Henry is) the best goalscorer ever in Arsenal’s history, so it doesn’t mean he will score as many goals but why not?
“I would say (Aubameyang is most like) Thierry Henry with his quality of runs. But it’s a bit too early to compare him to the best player ever who played here.
“He has played one game. But it’s a good example to follow. His finish was brilliant. His finishing is good. You don’t score by coincidence for so many years, if you score many goals.”
Aubameyang’s goalscoring record at Dortmund was impressive, 98 goals in 144 Bundesliga appearances, but Wenger also knows that does not guarantee goals in the Premier League.
“What we have observed is that the transfer nowadays from the goals scored in other leagues does not necessarily transfer 100 per cent to the English Premier League,” he said.
“When we played at Swansea, we played against 10 men in the last 25 yards and that doesn’t exist anywhere in Europe. To be as prolific in the Premier League is today much more difficult.”
— Arsenal FC (@Arsenal) February 9, 2018
Provided by Press Association Sport