Heaton and Keane are away with England this week, with the latter's club performances helping him to win a first Three Lions cap in the friendly with Germany on Wednesday night.
The English center-back was on worldwide duty, completing 90 minutes in the 1-0 defeat to Germany on Wednesday, when he addressed the reports.
England new-boy Michael Keane has admitted he is "flattered" by the reported interest in him from Merseyside rivals Everton and Liverpool in the wake of his worldwide debut. We've got nine games left in the season and we need to make sure we remain in the league.
The 24-year-old will be a wanted man, having impressed at Turf Moor this season and made his senior England debut against Germany in Dortmund in midweek.
And according to the Daily Mail, the centre-back has caught the attention of a host of Premier League sides, with Chelsea, Leicester City, Manchester City, as well as the Merseyside duo, all interested in Keane.
Burnley know at this point that they are destined to lose one of their best players in the summer and despite offering him a new contract that would see him become their highest-paid player, his priority is to win silverware.
Keane was a product of Manchester United's illustrious academy, but failed to establish himself as an important member of their squad and subsequently joined Burnley.
Burnley boss Sean Dyche is delighted for Michael Keane over his England debut.