Scott Arfield has scored 22 goals since joining Burnley in 2013
Dean Marney and Scott Arfield will leave Burnley as free agents at the end of the season.
Canada international Arfield, 29, has been given permission to speak to Rangers about a move back to Scotland, where he was born.
The ex-Falkirk man has played 194 times for Burnley in five seasons.
Marney, Burnley's second longest serving player after Kevin Long, has attracted interest from Championship side Nottingham Forest.
He has made 221 appearances for Sean Dyche's side since arriving from Hull City in 2010 but has struggled to regain a first-team place after suffering a cruciate ligament injury in 2017.
"We have to allow these lads the right and the chance to align their futures and honour the fact they've been fantastic servants to us, as well," said Dyche.
"I have nothing but respect for the people and the players and, therefore, if we can help them along the way and be open-minded about their next moves, and who they're speaking to, then we'll certainly do that."
On Arfield's potential move to Ibrox, Dyche added: "Rangers came through and asked us about Scotty Arfield, what his position was.
"Scotty was a boyhood Rangers fan. That one's pretty simple in its form if they want to speak to him. We said, 'Yes, of course'. We understand it."
Source: bbc.com