Manchester United continue to be linked with a move to Republic of Ireland defender Coleman during the January transfer window, while Eto'o is reportedly a target for Serie A club Sampdoria.
Everton manager Martinez rubbished reports that Coleman could be on his way to Old Trafford and said there have been no offers for striker Eto'o, who only joined the Merseyside club in August.
When asked about the possibility of Coleman moving on, he said at a press conference on Monday: "No, I said before that we are in a position that all that matters is to get a good momentum in the league and be as strong as we can be in the cups.
"Obviously we are not entertaining that sort of speculation of big sales, we are not going to sell our big assets that we have at the football club in the January window. All those stories or efforts, or admiration from the outside is just a waste of time really."
Sampdoria were reported to have agreed an 18-month deal for Eto'o, but Martinez insisted that is not the case.
He added: "I know there has been a lot of speculation, but we haven't been contacted, we have had no conversations about that issue at all.
"At the moment Samuel is working really, really well, he is always a really strong influence in the day-to-day work and there is nothing to comment really."
The Spaniard confirmed he is in the market for a goalkeeper this month and enquiries have been made, but denied that Cardiff City's David Marshall is a target.
‘Maybe I’ll be signed by Wrexham, who knows? English football would suit me – if an offer came, I wouldn’t think twice, I’d go immediately’ Euro 2024 cult hero reveals his UK dream
‘Managing Leeds? It was an option that appeared, but it wasn’t the right timing. I decided it wasn’t a good idea to leave the club I was at mid-season’: Premier League boss admits to turning down opportunity to replace Jesse Marsch in 2023
