The 25-year-old has been an ever-present in the league so far this season, his first at Upton Park following a summer move from Ipswich.
Having twice been named in the Championship team of the year Cresswell has continued to impress in the top flight and has reportedly caught the attention of some of the league's biggest sides, with City and Chelsea both believed to have taken a look at the former Tranmere man.
But Allardyce, who takes his Hammers to relegation-threatened QPR this weekend with only one win in their last 12 outings, believes Cresswell should remain at West Ham and continue his progression rather than seek a move.
Asked if Cresswell would be better off staying at Upton Park, the Hammers boss said: "There's no doubt about that because he's year one in the Premier League
"Year one is an ongoing experience that you have that you know the level
Aaron now needs to grow from that experience
His challenge is to continue to work even harder than he has this year, not to rest on his laurels.
"We have seen players do that and then year two is more of a disaster than his impressive first year
His professionalism will come into play at the start of next year by where he gets and if he gets to the next level."
Cresswell has not represented England at youth level but there were calls for his inclusion in Roy Hodgson's squad to face Lithuania and Italy last month.
Although he was not called up, he has continued to shine for the Hammers and scored a free-kick in their recent 1-1 draw at home to Stoke.
Recently quoted as saying he is "very happy" at West Ham, it is unlikely Cresswell would be angling for a move and, with four years remaining on his current contract, Allardyce has dismissed reports that the club may struggle to hold on to the left-back.
"As far as I am concerned, no one has bid for Aaron Cresswell," he added.
"It's all pure rumours and speculation
My problem is does it affect Aaron Cresswell and affect his performance?
"That's for me to make sure Aaron does what he can all season and he performs on a consistent basis
What will happen in the summer, we will wait and see
I have even heard somebody said we have put a £25million buy-out on him.
"That's the first I know, I haven't heard anything through the owners to say 'well, if somebody wants Aaron Cresswell they would have to pay £25million'."
Cresswell is likely to keep his unbroken Premier League appearance run in this weekend's London derby at Loftus Road - but Allardyce will still be without strikers Andy Carroll and Enner Valencia, whilst James Tomkins and Guy Demel are missing from a depleted defence.
Source : PA
Source: PA