The Spaniard is also wanted by Everton and Tottenham after impressing in a loan spell at Goodison Park during the 2018/19 season.
Gomes made 27 Premier League appearances for Marco Silva’s side as they finished eighth.
Sky Sports reports that Barcelona are keen to offload the 25-year-old this summer, but are holding out for a fee between £25million and £35million.
Earlier this month, Silva revealed his desire to sign loan stars Gomes and Kurt Zouma on permanent deals.
“I have a relationship with both,” he said.
“With both it is really good and really honest, until now I didn’t have one sign coming from them they don’t want be here.
“I am not saying they won’t change their mind tomorrow, three days or a week, but since we started to plan something their opinion has been really important.
“I have to have in mind what is their opinion when I plan. Let’s see what will be the decision, not just for them, but with their clubs.
“We are happy with them because they did well. We as a club and we as a technical staff really helped them both, it is clear.