Last week's joint £28m offer for the pair from Manchester United was dismissed out of hand as "insulting", and there has been no improved bid from Old Trafford.
Everton have at times failed to hold on to talent in recent years, losing the likes of Jack Rodwell, Joleon Lescott and - before that - Wayne Rooney.
But Martinez is certain the club is now in a position to stand firm.
He said: "There's been no other news. I know there's going to be talk about the transfer window but that's not what we're focusing on now.
"We are in a position where we don't have to sell. I don't think there's been any misguidance. We know exactly where we are internally. We're very, very strong financially, and we don't have to sell at all."
Martinez, meanwhile, has denied making a bid for Wigan midfielder James McCarthy.
The Republic of Ireland international has been linked with a move to Merseyside ever since Martinez left the DW Stadium to become David Moyes' replacement.
Martinez signed McCarthy during his time at Wigan and remains a big fan, but he said: "There has been no bid made.
"I think it's quite easy to understand that James is a player I signed at a young age and I've got huge admiration for him, so it doesn't take anyone (much) to create a little bit of a story. But there has been no bid."