West Brom will demand over £20million each for Craig Dawson and Jay Rodriguez.
Burnley have reportedly offered £25million for the pair, well below the asking price Press Association Sport understands.
Bournemouth are also interested in Rodriguez, who scored 11 goals last season as the Baggies were relegated from the Premier League.
Rodriguez has no release clause unlike Salomon Rondon who can leave for £16.5milion and Nacer Chadli for £17million.
Albion do not want to lose him and it would take a sizeable bid for them to considering parting with the striker, who only joined from Southampton last summer.
He spent five years at Burnley and scored 41 goals after being a trainee at Turf Moor before leaving for Southampton for £6million in 2012.
The 28-year-old left St Mary’s after being frustrated due to a lack of first-team action but despite Burnley being his home-town club, Press Association Sport understands he has not ruled out making a return to the south coast should Bournemouth firm up their interest.
Dawson, 28, made 32 appearances for the Baggies last season and joined from Rochdale in 2010.
He has become a dependable defender at The Hawthorns and can play at right back or centre back.
Albion have already lost Jonny Evans for a cut-price £3.5million after the defender joined Leicester last week.
Burnley are preparing for European football for the first time after qualifying for the Europa League after finishing seventh in the Premier League last season.