The San Sebastian-based outfit finished fourth and qualified for the Champions League next term and that has meant many of their squad have come under the microscope.
"We are not going to pretend that a team that finished fourth and has two players in the Best XI of the Under-21 European Championships is going to have nobody interested in their players. One thing leads to another," Arraste said.
In recent weeks Arsenal have been joined by Real Madrid in being linked with Illarramendi and la Real's trainer admits that the Spanish giants' interest is known.
"It is true that we are talking about one of the biggest clubs in the world, both in economic and sporting terms," he continued.
"However, we are not going to negotiate for him. He is not for sale. The club has made it clear, and I think the player has too, that we are not going to discuss hypothetical situations."
Real Sociedad have seen other players linked with moves away, but Arraste is confident that Illarramendi and several other key players will stay put.
"This is the same as it was with Loren and Aperribay. Illarramendi has said he is very happy here and I have talked to him about in person and is very excited about the coming season," he added.
"There is no plan B for us with him and he will be with us for pre-season training on Thursday.
"We want to maintain the main body of the team and add one or two more players to increase the quality."