Arfield has six months left on his current deal and is reportedly attracting the attention of a number of the Clarets' Premier League rivals, including Saturday's opponents Crystal Palace.
Dyche told reporters: "We have had talks with him and he has sat tight on an offer so we will keep an open mind and we will see what comes next.
"Scott knows where it all stands and he knows the club's situation. He's been a very, very good player for us and he continues to be."
Arfield is set to miss Burnley's trip to Selhurst Park with a minor knock but Dyche insisted he fully respects the Canada international's decision to consider the club's offer.
Dyche added: "We stay in contact with all the players and their agents and try to keep the lines of communication open.
"Every player has a right to decide what their thoughts are. He's done well for us and continues to do so but both parties have to agree and that's what it comes down to."