The paper claims the Scottish midfielder is torn over whether to end his relationship with Manchester United, which has spanned nearly two decades.
West Ham arguably represent a much better proposition for him in terms of playing regularly, with Manchester United boss Louis van Gaal enjoying a plethora of midfield options at Old Trafford.
The Telegraph suggests that the main rivals to West Ham in terms of signing the player at West Brom, with a £1.5 million fee mentioned.
If West Ham can secure the services of Fletcher then he could be a terrific capture for the club for several reasons.
He’s got plenty of Premier League experience and would offer Sam Allardyce a different option to the quality he already has across the middle of his team.
His leadership qualities may also appeal to the Hammers because Fletcher has led United on more than one occasion and has also been skipper of the Scottish national side.
It will be interesting to see which side he chooses.