The 22-year-old midfielder is also reported to be attracting interest from Blackpool after leading his side to promotion via the play-offs last season.
Manager Steve Davis admitted that he has spoken to Westwood about his future but warned that Crewe will not sell the latest in a long line of youth-team products unless his valuation is met.
"We have had a couple of enquiries about Ashley, but it has been nowhere near the amount of clubs that are being reported," Davis told the club's official website.
"He is a contracted player at Crewe and like all our players we would only consider selling if our valuation is met and it is a good career move for the player.
"I will be happy when the window closes and hopefully we will have everyone still with us."
Davis added: "I've had a chat with Ash because I think the speculation has been unsettling for him and affected his performance a little at Brentford on Saturday.
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We had a good chat and he responded with his usual performance at West Ham. He has been professional about it and got on with it."
Westwood has made more than 100 league appearances for Crewe since making his debut back in 2008. The Railwaymen have already lost teenager Nick Powell to Manchester United this summer.