The 25-year-old midfielder arrived at Goodison Park this summer, joining from Barcelona on a season-long loan.
Gomes, capped 25 times for Portugal, missed the first eight games of the Premier League campaign due to a muscle injury, according to Transfermarkt.
However, he was drafted into Everton's starting XI against Crystal Palace and since then has started every game for Marco Silva's side.
In his first game, Gomes played 82 minutes before being substituted, but he completed the full 90 minutes in the six successive matches (Transfermarkt).
Some Toffees fans are already in love with Gomes' talent and skills, and have already called on the club to sign him permanently next year:
We seriously need to sign him on a permanent deal before other clubs sign him— Steve (@Ste_133Efc) December 4, 2018
Sign him, no excuses just get it done— Alex Mackay (@alexmac55) December 4, 2018
Would rather see him sitting at a table signing a contract on a 5 year deal with brands arm around him— Will (@WAJG_96) December 4, 2018
Silva, however, has played down the prospect of Everton securing Gomes' signature on a permanent contract by saying his future is out of the club's control.
"He's enjoyed his first two months but let's see what we can do. We are working on that, I don't know if I have an answer in one week or two weeks," Silva told Sky Sports News ahead of Monday's Premier League game against Watford.
"It is not something that it is in our hands. The best scenario to look at is - it is not just in our hands as a club, not just in the hands of Andre, there is a third party as well. Barcelona are included, let's see when we can talk about the situation."
Gomes is contracted to Camp Nou until June 2021 and is valued at £13.5million by Transfermarkt, though the valuation dates back to May.