The Potters were in negotiations with the Hammers leading up to last Wednesday's transfer window deadline but missed out because of the player's wish to remain in London. Parker eventually signed for Tottenham, with Pulis having to content himself with the signing of Spurs duo Wilson Palacios and Peter Crouch and Birmingham's Cameron Jerome.
"We did have a go for Parker. It was something we were trying to do for a few weeks," said the Stoke boss in The Sentinel.
"But we realised that if he could, he wanted to stay in London. That was a big part of it with him.
"I felt there were certain areas of the team we can improve and have to improve and that was one of them.
"I enquired about him and kept in touch with Sam Allardyce (West Ham manager) to find out what the situation was.
"But Sam said Parker would prefer to stay in London because he'd got three boys in school there."
Pulis plans to offload some of his playing staff to npower Championship clubs in the coming week after Danny Collins, Danny Pugh, Michael Tonge, Andrew Davies and Tom Soares were all omitted from the final Premier League and Europa League squads.
The Stoke boss also left Jonathan Woodgate - a free transfer this summer after being released by Spurs following two seasons of injury problems - out of his European squad but that was for altogether different reasons.
"I don't want him to do the travelling," Pulis added. "If he can play 30 games in the Premier League, I'll be absolutely over the moon."
Source: PA
Source: PA