Forest keen to hang on to Jenas
The 29-year-old Tottenham player concluded his one-month temporary deal with a goal during a 4-1 victory at Barnsley on Saturday.
O'Driscoll says Jenas' contributions on and off the pitch have proved vital since his arrival and is planning on approaching Spurs over a possible extension.
"His (Jenas) attitude has been great,” O'Driscoll told Forest's official website.
"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.
"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.
"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' original spell at Forest saw him make 29 first-team appearances for the club before leaving for Newcastle in 2002.