The 33-year-old has lost his place in the Rovers team to Jake Kean and the club are prepared to listen to offers for the former England stopper, The London Evening Standard reports.
It is thought the Championship outfit are interested in cashing in on one of its highest earners. Robinson has three and a half years to run on his current deal at Ewood Park.
A transfer to West Ham would see Robinson reunited with Sam Allardyce. The Hammers boss worked with the former Tottenham keeper at Blackburn and rates him highly.
At present Allardyce has just two senior goalkeepers at his disposal, with Jussi Jaaskelainen as first choice and Switzerland Under‑19 international Raphael Spiegel as back up.
Stephen Henderson’s emergency loan spell at Ipswich has ended and the goalkeeper is expected to return to West Ham for extra cover.
Meanwhile, the Hammers have reportedly taken American international Graham Zusi on trial.
The 26-year-old midfielder is currently playing in Major League Soccer for Sporting Kansas City.
Zusi is regarded one of the best attacking midfielders in the league, and was named third in the MLS’ Player of the Year awards recently.
According to Sky Sports reports, the player was being tracked by several European clubs.
Zusi, who has three years left on his current contract, is now set to spend the next week with West Ham with a view to a permanent move to Upton Park.
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