The 33-year-old was one of the stars of the Rojiblancos’ La Liga winning and Champions League final reaching campaign, but his future at the Vicente Calderon is far from clear.
Despite manager Diego Simeone known to be fan of the 33-year-old, Tiago looks set to leave Madrid in the coming weeks when his contract expires.
Jose Mourinho is looking likely to lose David Luiz – whom he has frequently played in a holding midfield role – and it thought to be on the lookout for a replacement.
He is familiar with the experienced enforcer having signed him for Chelsea back in 2004, and could be tempted by a reunion.
The former Portuguese international would represent a risk free option for Mourinho, who would not be required to allocate any of his transfer funds to a deal.
Tiago himself is thought to be ready to make the move, with the Blues representing what is likely to be his last opportunity for a big contract.