Striker Martin Paterson held talks with the club over his Turf Moor future last night.
Paterson, 26 last Friday, is out of contract at the end of June, and Burnley have shown a willingness to extend his stay at Turf Moor.
The Northern Ireland joined the club for an initial £1min the summ er of 2008 on a three-year deal, which was extended after relegation from the Premier League in 2010.
And after his best season in terms of goals and avoiding injury since his first year with the club saw him score 19 on the way to promotion to the top flight and the Carling Cup semi-final, Burnley are keen to retain his services.
The former Stoke and Scunthorpe forward hit eight goals for Burnley - including two in the last two games of the campaign against Wolves and Ipswich - to add to his first for his country against Finland in August.
Following promotion, Paterson was dogged by injury for the next three years, with a knee problem forcing him to miss four months of the Premier League season.
He then made only 30 appearances in the following two seasons back in the Championship due to recurring thigh and hamstring injuries.
However, Paterson made 39 appearances this term, and Burnley turned down a loan bid from Wolves.