Mina and Gomes are yet to be seen in an Everton shirt since their arrival from Barcelona in the summer window, but they are now fit to play and Silva will not hesitate to use them.
"It is possible [they may be involved on Sunday]," Silva said.
"Andre is working hard as well. Mina the same situation and James as well, but like you know, the injury to James is a little bit different. But he is working hard.
"Of course [it has been frustrating]. Not just those three. Of course, for me as a coach, it's better when you have all players available to play to work with strong competition between them to achieve what you want.
"It's a good headache to decide the squad on Sunday and the starting eleven."
However, Mina may have to wait for his chance following the recent form of Michael Keane and Kurt Zouma at the back. When asked about the pair's form, Silva said: "Yes, I agree with you.
"But this is what I want, competition, and I have to take the decision. [Keane and Zouma] are doing well, we are being more solid in the last games as well as a team, not just the two central defenders, but as a team."