Cresswell joined from Ipswich Town in July and has made a seamless transition to the Premier League.
That has led to suggestions of a move elsewhere, with rumours suggesting Chelsea may allow Filipe Luis to rejoin Atletico Madrid and swoop for Cresswell as a replacement.
The left-back stated on Wednesday that he was committed to the cause at Upton Park and manager Allardyce is focused purely on helping Cresswell maintain his form.
"As far as I'm concerned nobody has bid for Aaron Cresswell so it's pure rumours that has to fill the media space," he said.
"It's for me to make sure that Aaron continues to do what he has done all season, which is perform on a consistent basis.
"He has to continue to work as hard as he can, not rest on his laurels and build on the impressive year he's had."
