However, if they don’t move swiftly, they could risk losing out to their La Liga rivals.
Madrid are starting to consider options to replace a 32-year-old Luka Modric.
Eriksen has been in sensational form this season, hitting double figures for goals and assists in the Premier League.
Buffon, 40, called time on a legendary 17-year association with the Turin giants at the end of 2017/18. But he swiftly declared that he had no intention of retiring.
Corriere dello Sport have stated a multi-year contract worth €8 million (Dh34.1m) per annum is now about to be signed with the Ligue 1 champions.
If this comes to fruition, he will be expected to share goalkeeping duties with France’s World Cup 2018 call-up, Alphonse Areola.
In-demand Ajax youngster Justin Kluivert has declared he is not “100-per-cent convinced yet” to depart the Eredivisie outfit, despite publicly criticising them recently and being linked to a host of European heavyweights.
Kluivert, 19, scored 10 goals in 30 appearances for the Amsterdam side in 2017/18. Such form has reportedly alerted the likes of Barcelona, Manchester United and Roma to his talents.
These rumours increased earlier this month when he accused the Ajax hierarchy of trying to force him to sign a new contract so that he would command a greater transfer fee.
But in an interview with FOX Sports, the forward appeared to be open to a shock U-turn.
He said: “There are exciting moments coming for me. Let’s see what they’re going to be.
“In the end, it’s my decision. I’m not a 100-per-cent convinced yet. I have to think things through. To stay at Ajax is definitely an option. It certainly is.”