Initial talks with the 29-year-old will take place in Edinburgh, although Ipswich Town are one of seven other clubs in England and abroad also competing for his signature.
Lafferty was released by Norwich City last month and is interested in moving back to Scotland. He spent four years with Rangers between 2008 and 2012 and has since played in Switzerland, Italy, England and Turkey.
Hearts want him to lead their attack next season but would need to offer a deal to make him one of their highest-paid players. More money will be on offer in England and abroad for a forward who has scored 20 goals in 61 appearances for Northern Ireland, making him their second-top scorer of all time.
Lafferty will meet Hearts officials to gain a feel for the club before deciding whether to take things further. He is already well acquainted with the Tynecastle assistant coach, Austin MacPhee, who is also a member of the Northern Ireland coaching staff. Bringing the player to Edinburgh would be regarded as a genuine coup but, with such strong competition, much will depend on Lafferty’s salary demands.
Ipswich are keen to take him to Portman Road, whilst the Azerbaijan champions Qarabag have also declared an interest.