The Northern Irish international spent a four year period at Ibrox between 2008 and 2012 in which he made over 100 appearances, and now Steven Gerrard wants him to return to the club.
Lafferty scored 19 times in all competitions for Hearts last season, and as a result attracted the attention of the Rangers boss as he looks to strengthen his attacking options, something that has been mentioned as an area of weakness in the side.
An initial offer of £200,000 was rejected by Lafferty's current club, with Rangers set to table another offer to try and secure the forward's services.
Gerrard is also thought to be interested in bringing Man City's Kean Bryan on loan, given his versatility in being able to play in midfield or defence.
There have already been 10 new signings under Gerrard's leadership, as the former Liverpool and England captain looks to challenge city rivals Celtic in the Scottish Premiership in his first season in senior management.