Arfield, who has been with the Clarets since 2013, has been given permission to speak to Rangers about a move back to Scotland, his country of birth.
Meanwhile, Marney - Burnley's second longest serving player after Kevin Long - has reportedly attracted interest from Championship side Nottingham Forest.
"Both are tremendous servants for the club and if their futures can be aligned in a simple process, we would obviously be open to that," Dyche told reporters on Thursday.
"It's important for any player here. We try to be really fair with our players but particularly ones who have done what they've done - for themselves, for me, for the team and the club.
"Rangers asked us about Scotty Arfield and what his position was. Scotty was a boyhood Rangers fan and that one's pretty simple in its form if they want to speak to him. We said: 'Yeah, of course. We understand it'.
"Dean Marney's searching for the next challenge and what's coming his way. A couple of managers have spoken to him with possibilities. He's fit, he's well, he's been involved with us. We're certainly respectful, as we are with everyone here.
"These are two players who have done a lot for this football club and obviously we hope things work out in their favour."
Burnley will qualify for next season's Europa League if they can defeat Brighton & Hove Albion on Saturday as a result of Manchester United and Chelsea meeting in the FA Cup final.