Lescott, who earned 26 caps for England during his professional career, has claimed that Abraham leaving west London would not come as too much of a surprise.
"I think he [Abraham] has made it known that he's not convinced about signing a new contract," said Lescott.
"Obviously, players want to play. He's had an experience of playing, he's been on loan and done the hard yards in the lower leagues and come back to Chelsea and performed.
"He's not necessarily played badly, but for whatever reason he hasn't been given opportunities by [Thomas] Tuchel.
"Do I see him being there long-term? I don't, to be honest. I see him having to go away. We've seen that in the past with Chelsea.
"I'm sure Chelsea would love to have Romelu Lukaku right now, but he had to go elsewhere. It would be slightly naive of Chelsea to think they don't need a Tammy Abraham because he's proven that he can score goals.
"I'd like to see him stick around, but I don't see it happening."