Fullback Gaya has been linked with Barcelona, while midfielder Soler is regarded the club's most saleable asset.
But Bordalas says: "They are our captains, they feel Valencia and they have a tremendous commitment. We have no doubt that they will continue with us.
"The club is not going to give away any player."
Bordalas is set to speak with Valencia owner Peter Lim in the coming days for the first time.
“He is the owner of the club but we have a president (Anil Murthy) with whom I speak every day, with whom we are in good agreement. I have not spoken with Lim, but I believe that in the next few days we will meet electronically. It will be a pleasure to meet him."