The Hammers are desperate to take the Pompey boss to Upton Park.
But their efforts to lure Redknapp back to his former club look destined to fail.
The News understands the London club placed Redknapp at the head of their shortlist to replace Alan Curbishley.
Dutchman Frank Rijkaard and Everton boss David Moyes are their other major targets to succeed Curbishley.
Any official attempt to land Redknapp would be given short shrift by the Blues.
And West Ham lack the financial might to untie the man who carried Pompey to FA Cup victory earlier this year from a lucrative contract.
>>> Take a look at our Pompey blogs and get involved. Click here.Redknapp signed a deal back in October tying him to the club until 2011.
That contract was reported to be worth well in excess of £2m per year with bonuses.
West Ham lack the muscle to compensate Pompey for that as well as offering him a similar deal.
An offer to return to the club where he spent the vast majority of his career would have proven tempting to Redknapp, though.
He is settled with Pompey after turning down the chance to manager Newcastle in January.
And he this week spoke of his comfort in his current role, and the fact he can go about his job without outside interference – a factor in Curbishley quitting.
But Redknapp still retains a huge affinity for his ex-club.
He spent his youth with West Ham, signing professional forms in 1964 and spending eight years there as a player.
Redknapp later enjoyed another seven years with the club when he succeeded Billy Bonds as boss in 1994.
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The full article contains 318 words and appears in The News newspaper.