Adebayor is a free agent after his release from Tottenham last year, although the North London side are still paying his wages.
Jenas played alongside the striker at Spurs, and believes he would be a worthwhile investment for teams at both ends of the table, even suggesting Manchester United make a move.
He said: "If I were a Premier League manager in need of goals this month, I would break the bank to get Adebayor for the next six months. And there are a lot of clubs that fall into that category: Crystal Palace, Man Utd, Norwich, Newcastle.
"These kinds of clubs could do a lot worse than signing Adebayor on a short-term deal. And for those near the bottom, he will almost guarantee you safety."
Crystal Palace are the side which do have a genuine interest in the striker, with manager Alan Pardew admitting the club are entertaining a deal, reported The BBC.
The Mail reported last week that Adebayor wants to sign with a club in the south east of England, which would rule out both Newcastle and Manchester United, although it is hard to see him turning down the chance to sign with the Red Devils.
BBC pundit Jenas also told Yahoo Sport that the reason Adebayor failed at Spurs was due to poor man management and clashes with authority figures, which makes it questionable whether he would be suitable tough taskmaster Louis van Gaal at Old Trafford.