The Uruguayan has by turns in the past week seemed destined to sign for Valencia and then West Ham but now Julio Insa of Radio Esport in the Spanish city has tweeted that the Blues are now in the running as well.
They are aware that they can not compete financially with West Ham but are determined to fight it out to get Gomez to the Mestalla ahead of the new season.
The Austrian wanted to leave for the Far East in January after a £200,000-a-week offer from an unnamed Chinese club but West Ham convinced him to stay. Has offer from Chinese club.
West Brom are looking to sell Rondon this summer and with clubs keen to bring him in, it is highly unlikely that the Venezuelan will be seen in West Brom colours ever again.
Our partners at Sky Sports are reporting that Celta Vigo had agreed a deal with Valencia for the transfer of Gomez, as the La Liga strugglers would receive $20 million and three Valencia players (including former Celta star Santi Mina) in part-exchange for Gomez moving to the Mestalla. In real terms, there was not much difference between Wolves in seventh and West Ham who eventually finished 11.
West Ham have placed a £40m price tag on Austrian striker Marko Arnautovic following his submission of a transfer request earlier in July. To have any chance of achieving their objectives next season, they have to add a forward to their squad.
His brother, Danijel, has now agitated the West Ham hierarchy by suggesting the club are treating Arnautovic like a "number".