Nastasic has been widely expected to leave the Etihad Stadium after falling down the pecking order, while Richards has struggled to cement a starting spot at City for the last few seasons.
"Matija needs to play," the Manchester Evening News quotes Pellegrini as saying. "We already have important players here with four full backs, [Martin] Demichelis, [Vincent] Kompany, [Eliaquim] Mangala and [Dedryck] Boyata.
"So we will see in the next few days what happens with Nastasic. He is an important player, but he has offers and I think the best thing for him is to play.
"That also goes for Micah Richards, who didn't want to continue here because he wants to play more. He had a contract to renew but didn't want it."
The Chilean also stated that Sinclair and Guidetti could leave the club because he does not like to have too many players within his squad.
The English champions began the defence of their Premier League title with a 2-0 victory over Newcastle United at St James' Park on Sunday.