Hartley was dropped for the SPL game against Rangers |
Rangers are expected to increase their offer to Hearts for Paul Hartley on Wednesday in an attempt to win the services of the Scotland midfielder.
BBC Sport understands that Hearts have rejected Rangers' latest bid of £750,000 and appear to be demanding more than £1m for the 30-year-old.
Hartley was left out of last Saturday's SPL fixture between the sides at Ibrox.
Hearts head coach Valdas Ivanauskas said Hartley was omitted due to "football business".
That was thought to have been a bid from Rangers.
Hartley has two years of his contract to run and Celtic had a bid for the playmaker rejected last season.
The midfielder appeared in public alongside goalkeeper Craig Gordon and former captain Steven Pressley in October, when Pressley said there was "dressing-room unrest".
Pressley has since moved to Celtic, while Gordon was also dropped for Saturday's SPL game at Ibrox.
Rangers' attempt to sign Hartley could be boosted by the sale of Thomas Buffel.
The Belgian forward is in Hannover for signing talks with the German club.
Rangers could also sell Scotland midfielder Gavin Rae, who has attracted interest from several English clubs.