West Ham United, Crystal Palace and Brighton & Hove Albion have all been credited with an interest in the 28-year-old, who will see his current deal with Burnley expire at the end of this season.
Dyche, however, responded "no" when asked whether the Clarets had received any bids for the Canadian, and claimed that the club are still hopeful of reaching an agreement when it comes to a new deal.
"No. We've had talks with him. He's sat tight on an offer so we'll keep our open minds, as will he, I hope, to what comes next," Dyche told reporters.
Arfield joined Burnley from Huddersfield Town in 2013, and he is fast closing in on 200 appearances for the Clarets in all competitions.