Dominic King of MailSport has joined reporter Ian Abrahams in tweeting that the Blues have made a move for the 25-year-old who has also been strongly linked with West Ham in the last 48 hours.
Gomes was also the subject of speculation suggesting that he had been offered to Manchester United, perhaps along with Everton target Yerry Mina, as a make-weight in a bid for Paul Pogba.
There are no indications as yet whether the Blues' offer is to take Gomes on loan or on a permanent deal. He is currently out of action with a hamstring injury sustained on Barca's pre-season tour of the United States which might make a temporary move for him more likely.
Gomes, who made his name as a top player at Valencia, has reportedly been keen on a move the Premier League for a while and came close to joining Tottenham last year before the deal fell through.