Grimmer is available on a free transfer after seeing out his contract at Coventry earlier this summer.
The 25-year-old has spent the last two years at Coventry after joining from Fulham in 2017.
Grimmer was a key man in Coventry’s promotion to League One in the 2017/18 season and scored in the play-off final at Wembley Stadium in London.
Grimmer, who can operate at right-wing-back, right-back and centre-back, is an attractive proposition for clubs due to his versatility to play anywhere across the backline.
League One duo Bolton and Blackpool are both looking to bolster their defensive options ahead of the new season, and they have expressed an interest in the former Scotland Under-21 international.
League Two Exeter are keen to take Grimmer to St James Park, while a number of clubs from abroad have also made enquiries about the former Aberdeen man.
Grimmer is now assessing his options before making a decision on where to move this summer.