The 35-year-old, who played under Johnson at Bristol City, has not started a game since mid-October.
"I'd take Adebola tomorrow but we can't afford one of his boots," Johnson told BBC Radio Cambridgeshire.
"The club won't let him come here just to play games and the finances are way too much for us."
Posh are after a target-man to replace Dave Hibbert who dislocated his kneecap in Tuesday's FA Cup victory over Stockport.
"We're trying to find a big one with the mobility and the quality, but most of them are already playing in the Premiership," Johnson added.
"We do need numbers anyway. We are short in our numbers, especially if we're going to be as unlucky as we have been with injuries."
Hibbert, 24, has made just 11 appearances for Posh since arriving from Shrewsbury in the summer and is unlikely to add many more games to his tally this season.
"There's a lot of ligaments around it, including the cruciate ligaments and he's going to be out for some time," continued Johnson.
"He's still in his mid-20s, hopefully he'll come back at some stage, hopefully before the end of the season.
"But it's going to take a lot of rehabilitation for him to get back right."
Source: BBC Sport