The pair were the subject of a rejected double bid from the reigning Premier League champions earlier this month, with the offer subsequently described as "derisory" by Everton.
Goal understands the Red Devils have since submitted an improved bid for the duo with manager David Moyes urging Martinez to "do what [is] right for the players".
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However following his side's 0-0 draw with West Brom on Saturday, the Spaniard hit back at his predecessor.
"I think my comment is quite clear," he told reporters. "If managers start talking about players that are registered in other clubs then that's the end of the whole thing.
"I think everyone should look after their own things internally. I'm sure they've got many issues in the same manner and I could easily come out and give my opinion about his players but I think I'll be more respectful than that.
"The position we've got is we don't want to sell. So then you haven't got a figure. Everyone has got a price but when you see you invest money in a player and five years later you get offered the same money after performing really well, I think that becomes a bit of a nonsense.
"The last thing I want is to get into a media war with a manager I really respect. I think the business should be done quietly but it's very unfortunate when you read papers and people talk about your players.
"I could sit down here and give you half an hour of my vision of how the other club is being run, the players that they want to go and how they should be sending all the messages to all the clubs around the world that they've been trying to sign players and they haven't been able to do it."
And, on Fellaini and Baines' performance in the draw with West Brom, Martinez added: "On the outside there's a lot of talk and speculation but as you can imagine internally we are focusing on the games.
"We need to concentrate on working hard and getting ourselves as good as we can. I never had a doubt because they are two professionals, they are two ambassadors of Everton, they have been here for a long time and they know how to perform and give everything they have."
The former Wigan manager also questioned the fairness of allowing the transfer window to overlap with the start of each new Premier League campaign, with three fixtures scheduled prior to its close on September 2.
"I've said it a few times, I think it's very unfair to play competitive games when the window is open," he continued.
"I hope the authorities will look into it because it's going to get worse. You're looking at next season we've got the World Cup final on July 13 and the first league game on August 7 - you're going to have a full month of speculation.
"Many teams will have a starting XI on August 7 and maybe five or six changes by September 2 the way it's going."