Guardiola's side have been looking to sign the former Chelsea striker.
are reportedly not making an offer for former
Although the January transfer window closed on Monday, clubs are still looking to sign free agents like Costa.
According to sky sports, the top six teams in the
, whose names have not been revealed, gave the former Chelsea man the opportunity to return to England within the deadline day.
Further reports indicated that
, currently fifth in the top flight table, were monitoring Costa.
In recent weeks, Manchester City have been in contact with Costa, but the Daily Mail writes thatPep Guardiola
's side are not interested.
There have been suggestions that Costa could be on his way to Etihad Stadium given the issues facing the City.
has missed most of the season due to injury and illness, and
spends considerable time on the sidelines.
But Costa turns 33 this year, and there have been concerns about his fitness.
Former City defender
has asked his old club to sign costa, but they do not seem to heed his advice.
"Why not get him in until the end of the season? He would do more than just ruffle a few feathers and be a pain in the backside for opposition defenses - he is a proven finisher who would offer Pep Guardiola's side a proper plan B," Richards told BBC Sport.
"When I won the title with City in 2012, we had four strikers at the top of their game - Sergio Aguero, Carlos Tevez, Edin Dzeko and Mario Balotelli. They all played a big part at different times of that campaign.
"Now? They still have Aguero of course, but there are huge question marks over his fitness, with Gabriel Jesus the only alternative."