Demichelis, who joined City in the opening weeks of last season, has overcome a difficult start at the Etihad Stadium to establish himself as a key member of the champions' rearguard.
The 34-year-old Argentinian is out of contract at the end of the campaign but Pellegrini, who has worked with the player at two previous clubs, is keen for him to stay.
Pellegrini said: "We will see, in the next days maybe he can renew his contract.
"I think Martin is a very important player for our squad, he is an experienced player, he is a leader of our group
He wants to stay
Probably, he will sign another contract."
Demichelis, a former Bayern Munich centre-back, played for Pellegrini at River Plate and Malaga before following him to City after a strange, brief stint at Atletico Madrid, where he did not play a single game.
Pellegrini's suggestions of a new deal come a year after Demichelis' City career hit its nadir with his sending off against Barcelona.
Demichelis' early City performances were unimpressive and his dismissal in the Champions League last-16 tie first leg at the Etihad Stadium - a fixture which is repeated next week - attracted considerable criticism.
But he bounced back with some commanding performances in City's successful Barclays Premier League title run-in and he is now likely to be rewarded with an extension.
City's other major contract issue at present concerns midfielder James Milner.
The club have been in discussions with the England international, who also becomes a free agent in the summer, for some time but no new deal has yet been agreed.
Milner has impressed in a variety of positions this season and Pellegrini wants him to stay.
The 29-year-old is reportedly happy with the terms on offer but the sticking point is thought to relate to playing opportunities.
The versatile Milner is also City's chief injury doubt for Tuesday's visit of Barcelona with a knee problem.
City are hopeful the injury is not serious but he has been ruled out of Saturday's home encounter with Newcastle and will be assessed in the coming days.
Asked if he might be fit to face Barca, Pellegrini said: "We will try
We'll see how he improves in the next days.
"He is talking with the doctor about all the situations
I don't think it will be very serious
He has a kick in his ligament in his knee."
Source : PA
Source: PA