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Gomes is likely to be available on a free transfer within the next month, after his Italian club Fiorentina failed to honour his contract.
The striker has not been paid since November and that allows him to break his contract and move on a free transfer. Gomes goes to a tribunal next month, with a view to getting his contract annulled.
He has already indicated that he would like a move to England. Xavier said: "It would be great for him and for Liverpool if he ended up joining us. I am quite certain he would be an outstanding signing.
"Nuno is a great goalscorer and also very technically gifted. Having played in England for three years myself, I have no doubt that his style of play would be perfectly suited to the Premiership.
"Hopefully with me around it would be another reason for choosing Liverpool, because having a fellow countryman at the club would help him settle in."
Xavier admitted his switch across Merseyside was a painful one. He said: "I hope that the guys at Everton understand my decision. I had a great time at Goodison but it was simply too good an opportunity to turn down."