The Wales captain returned to his native city of Cardiff on a season-long loan on Tuesday after being told by City that he was not in Roberto Mancini's plans.
Tottenham, Fulham, Celtic and Bolton were among a number of clubs who were interested in signing Bellamy, who, prior to his move to the Bluebirds, has played for seven different sides since starting his career at Norwich in 1996.
And Pulis has admitted that Stoke also made an approach with the offer of Premier League football, but they could not change the forward's mind regarding a return home with Championship outfit Cardiff.
"We inquired about Craig," Pulis told The Sentinel. "But unfortunately for us his main concern was getting back to Wales to be close to his young family.
"Cardiff is also his hometown club, so it all fitted for him to make that move instead of the other offers on the table for him.
"Craig is 31 now and has done a hell of a lot of moving over the years when you look at all the clubs he has played for.
"It would have been nice if we could have sorted something out because we all know what an asset he can be as a player.
"He brings skill and energy to any team, and is a born winner full of passion, which inspires those around him."
Source: Team Talk
Source: Team Talk