The AC Milan striker, who turns 41 next month, helped Silva’s old club win the Serie A title last season and the Brazilian, after turning 38 in the week, wants to prolong his career in a similar fashion.
“I talk often with Zlatan and recently more often because Chelsea will play against AC Milan in the Champions League,” he told the club website.
“My aim is to play until I'm 40 years old but I don’t know if it will be this level or this competition.
“It depends on this season and we’ll see what will happen in the World Cup. It also depends on a contract extension but yeah, my aim is to play until I’m 40.”
Silva’s Chelsea contract expires next summer but he remains a fan favourite having arrived on a free transfer from Paris Saint-Germain, where he spent several years with Ibrahimovic after a stint together in Milan.
The Swede made headlines last week for vowing to come back “with violence” when he finally recovers from knee surgery in the new year.
He told Gazzetta dello Sport: “If I see a player stronger than me, I'll stop. But I haven't seen him yet.”