Earlier this week, young Reds midfielder Jasper Moon, 20, signed a new two-year deal, with the academy product committing his future to the club until June 2023.
Palmer, 22, who became a regular under Valerien Ismael and enjoyed an impressive 2020-21 season which saw him make 39 appearances in all competitions, is contracted until next summer.
Adeboyejo, 23, who started in the Reds’ play-off second leg at Swansea City, had a one-year contract extension triggered in February, with his deal due to run out in the summer.
The former Leyton Orient player – who joined the club in the autumn of 2017 following a successful trial – appeared 38 times in all competitions for the Oakwell outfit last term.
Reds chief executive officer Dane Murphy said: “The ones we have spoken to and continue to speak to are Victor and Romal. We are continuing to work on extensions for both of them.
“It is just getting them onside and trying to make sure all parties think that it is agreeable, but it is heading into the right direction.”
On the club’s policy decision of getting young players under contract in the long-term, Murphy continued: “That is pre-planned and the structure of what we are trying to achieve.
“We are in better shape than most because we have longer-term contracts on our younger talented players.
“We have to make sure we continue to strengthen in the summer and continue to take the next steps to continue to compete at the highest level.
“We have done a lot of work already and have pre-planned and prepared for this window and are hoping to get everyone on site.”