The England midfielder’s initial month’s stay with The Reds came to an end after today’s impressive 4-1 win at Barnsley.
Jenas bagged Forest’s fourth goal and O’Driscoll is keen to see the Club strike a deal with Tottenham to keep him on Trentside longer.
The manager told us: “Sometimes as a manager you are wary about taking a big name from the Premier League, which he is, but he’s been first class.
“His attitude has been great, he’s got great experience and we’ve used his opinion on things because he has an influence on the group.
“The initial first month was a suck-it-and-see thing for both parties.
“We’ll have to revisit it over the weekend and see where we go but we’d like to keep him if we can.”
Jenas, who started his career with The Reds, set the seal on Forest’s impressive win at Barnsley by bagging their fourth goal after joining the action as a substitute.