The forward has attracted a number of Championship outfits but the boss will only see him leave for the right fee, and says he does not want to see Toffees become a selling club
The former Leeds United man has scored 10 goals since joining the Toffees last summer.
Leicester have been confirmed as one of the clubs interested, with Southampton and Nottingham Forest believed to be monitoring his situation, but after rejecting three separate bids for the attacker, Moyes has stated he will only sell him for the right price.
He told the press: "We had a £2 million bid from Leicester. We have had an offer from three clubs for Jermaine, but we've not had one offer which we consider coming close to what Jermaine is worth.
"I brought all the players here - everyone by me. I have a responsibility to them.
"There is not a club in the country who does not have a price for every player and if we got an offer big enough I would have to sell.
"But at the moment no-one has come in with an offer which has come close to making me consider it.
"I am not going to become a selling club, I am not here to do that, I am here to build a strong team and no-one will go unless I say so.
"If I get an offer which is right of course I will [sell]."
He added: "I would never put Everton in jeopardy and if we were getting in the situation one or two other clubs have got in then obviously I would have to do something but we are not in that situation."
With the London riots causing the Toffees’ clash with Tottenham last weekend to be postponed, Moyes’ side will start their season on Saturday afternoon against QPR.
This week, chairman and major shareholder Bill Kenwright admitted that Everton are operating on a shoestring budhet and are in need of investment, leading to fans questioning the ownership of the club.
Moyes on the other hand believes the theatre mogul is doing as best a job as he can and that the rest of the staff are committed to making Everton as good a club as any.
"There have been financial problems for the past four or five years, we have had not much money during then - this year is no different," he continued.
"What I have got is a brilliant group of players and a really good team. Of course, we would like to add to the squad - every manager wants to do so.
"A few years ago we had to trade some players like James McFadden and Andy Johnson but that's no different. Every manager has to do that at some point and not every manager will be gifted with loads of money.
"I think that we do our best with what we have got. We have a really good chairman who does everything he possibly can to make the club work."