I have a player in his last year of his contract.  I went to to give him a contract extension and he is stating his is testing the waters.  Is it possible that he will reconsider during the initial/team free agent phase or will he absolutely take it to the league wide free agent period?  Thanks, and I posted his profile below if that matters:

You will have a chance to make an offer. Make a high one if you want to keep him. I think I've read that can work. Don't count on him signing with you for his asking price. I don't think a player who says they will test FA ever signs for their asking price.

i should clarify that i am in season 22, cannot sign him to the extension in this season, and am wondering in season 23 if i will have a shot at him before everyone else.

Maybe.  There's a possibility he'll say "Unless you blow me away with an offer, I'm filing for FA."

I've signed a few of those guys.   I've added 50% and a year to the demands.