City manager Manuel Pellegrini reportedly wants the quartet to leave the Etihad and find new clubs before the end of the transfer window.
Serbia centre-half Nastasic has been linked with a move back to Italy, after joining from Fiorentina in August 2012, while Sweden forward Guidetti is wanted by Feyenoord in Holland.
Nastasic, 21, made 23 appearances last season his final one in the 1-0 home defeat by Chelsea in February. He played the whole of the Community Shield defeat to Arsenal but dropped out of the matchday squad for the Premier League opener at Newcastle.
Richards, 26, joined the club from Oldham as a 14-year-old but the England right-back made just 10 appearances last term, with the majority in cup competitions.
Sinclair, 25, spent the season on loan at West Brom, playing 11 times, and Guidetti, 22, spent five months at Stoke, making six appearances.
"Matija needs to play," said Pellegrini. "We already have important players here with four full-backs, Demichelis, Kompany, Mangala and 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.
"We will see what happens, but we have until the end of August to see what kind of offers we get for Matija.
"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.
"So we have three or four players extra - Scott Sinclair and John Guidetti are also important players - but I don't like to have so many in the squad.
"I think 22 players is enough and they are all players, who have a lot of quality. It is good for them to play."