The Tynecastle side rejected an offer of £200,000 which is considerably short of their valuation of the Northern Irishman.
The Ibrox side are seeking reinforcements up front and had earmarked the 30-year-old as a potential target ahead of the approach, according to STV.
In an interview with STV earlier this week, Gers chairman Dave King said: “I think we could probably see another couple coming in and possibly another couple going out just depending on what happens with the English window coming up.”
The “couple” of players mentioned are believed to be Lafferty, and Manchester Ciy defender Kean Bryan.
Rangers boss Steven Gerrard has already brought in Umar Sadiq on loan from Roma, but the towering striker is still some way off match fitness and while Alfredo Morelos scored the only goal in Croatia last night as Rangers recorded a 1-0 win over Osijek, Gerrard is understood to be keen on beefing up his attack even further.
Lafferty had a four-year spell with Rangers between 2008 and 2012, helping the club to three Scottish titles as well as one Scottish Cup and scoring more than 30 goals in the process.
Amid the financial turmoil at Ibrox in 2012, Lafferty became a free agent, and joined Swiss outfit Sion before moving on to Palermo in Italy a year later.
Norwich City was his next port of call but he found first team chances limited at Carrow Road and was loaned out to Turkish side Caykur Rizespor, and Birmingham City.
Lafferty was linked with both Hearts and Hibs last summer, but signed a two-year deal in Gorgie, scoring 19 goals in 41 games last season.