Abraham, 23, was a key player for former boss Frank Lampard and scored 18 goals in 47 appearances last season.
But Tuchel left Abraham out of his Chelsea squad to face Manchester United last weekend and Liverpool on Thursday night, leading to speculation over the forward’s future at Stamford Bridge.
Abraham has fallen behind Olivier Giroud and Timo Werner in the pecking order in west London and Lescott believes he will leave Chelsea sooner rather than later.
Lescott told Premier League productions: ‘I think he [Abraham] has made it known that he’s not convinced about signing a new contract. 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 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 he can score goals.
‘I’d like to see him stick around but I don’t see it happening.’
Explaining why he dropped Abraham for Chelsea’s Premier League clash against Manchester United, Tuchel said: ‘We have 21 strong players and only 18 possible in the squad.
‘Hard decisions, it’s my job to make hard decisions. This was the decision and Tammy was not with the group.
‘At the moment he is only struggling with my decision. We have a strong squad. We have only Thiago Silva injured that means we have to make hard decisions.
‘We have Kai Havertz who can play as a number nine so there was no need to bring a fourth number nine to the pitch.
‘Things are difficult for him. Things are not as easy as they should be for him in the moment and he will get full support. This was the decision.’