Portsmouth manager Grant is favourite to land the Hammers job but Sky Sports reports that owners David Sullivan and David Gold are also interested in Cardiff boss Jones, Blackpool's Holloway and Allardyce of Blackburn Rovers.
Jones and Holloway have both enjoyed successful seasons in the Championship, leading their clubs to the play-off final where they will meet each other on Saturday.
Allardyce led Blackburn to a top 10 Premier League finish and could make the move south to London.
Portsmouth administrator Andrew Andronikou has given Grant permission to talk to the Hammers about a deal.
"We'll sit down this week and have a discussion about his future," Andronikou was quoted as saying in The Daily Mail.
"I want to make it clear we will support which decision he comes to. He's given unconditional support for us over the last four months when maybe other managers would have walked.
"If he wants to leave we won't stand in his way. We'll give him our full support.
"We're not going to hold anyone to ransom. If he wants to move on we'll be behind that. I think all the fans would be behind that decision, too."
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