Reports in Italy claim Abraham, who has been linked with Arsenal and West Ham, could be poised to join former Blues boss Jose Mourinho at Roma.
Even before Lukaku came on to Chelsea’s radar, Abraham had struggled for game time since Tuchel took over at Stamford Bridge in January.
Although he is in the squad for Wednesday night’s Super Cup final against Villareal in Belfast, the 23-year-old could look to move on.
“He was clearly not happy with the last half a year and he has maybe reason not to be happy,” said Tuchel.
“Maybe it was my fault not to push him and trust him at the same level as other players. I can understand he wants more minutes, so the decision will be how do we plan?
“What are Tammy’s plans? Does he fight his way back into the team from the position he ended last season? Or does he want to change the club to one where he has a better chance of being a starter?
“I can understand and this is the situation. It’s quite a normal situation until the transfer window is closed. Tammy is one of the players where we constantly evaluate the situation and adapt to the needs.
“There is no news now, he is available for the starting XI tomorrow or to come off the bench.”
Tuchel refused to discuss the latest on Lukaku’s reportedly imminent £97million switch from Inter Milan back to the club he left in 2014.
But he did admit that the arrival of a big-money signing can have a detrimental effect on certain players.
“I think it is good for any squad if players with a certain quality or attitude arrive,” he added.
“At the same time, you need to be aware that not everybody is happy. If I am a defender and a big player arrives in my position, they might not be fully convinced about this arrival or even happy at all about it.
“I think this is pretty human and we have to take care about this.”
Tuchel may have been unwilling to talk about Lukaku but defender Antonio Rudiger was happy to share his experiences of playing against the Belgium striker.
“Obviously you can see the body type. He’s a beast,” said Rudiger.
“He’s someone who is very strong and I think also he showed it in Italy over the past two years.
“He did very well over there. And also for his national team. He’s a goalscorer and for me a top striker.”