Goodwillie is currently looking for a new club after being put up for sale by English Championship outfit Blackburn Rovers.
The 25-year-old has been loaned out three times during his disappointing spell at Ewood Park - to Crystal Palace, Dundee United and Blackpool.
The former Scotland internationalist has a year left on his contract with Rovers, but would consider another temporary move.
Rangers tried and failed to land the forward from United back in 2011 when Craig Whyte was in charge, after having a bid rejected by the Tannadice club.
Goodwillie, who was named Scottish Young Player of the Year in 2011, joined Blackburn in a £2.8 million transfer instead.
Gers boss Ally McCoist has already strengthened his front line at Ibrox by bringing in experienced Scotland striker Kenny Miller.
And McCoist has also been tipped to make a move for another former Light Blues hit man - free agent Kris Boyd.
The manager has clearly identified that adding to his front line is a priority this summer, due to the difficulties his team had in that important department last season.
The Rangers gaffer was forced to rely heavily on Nicky Clark, who spent a long spell out injured, and Jon Daly due to a lack of back-up.
An inability to score goals led to some wins that were tougher than they ought to have been, as well as disappointing results - including in the Ramsdens Cup final against Raith Rovers.
Rangers have also been tipped to make moves for former Scotland midfielder Don Cowie and centre-half Darren McGregor.
Cowie is currently without a deal after his contract with Cardiff City, who were relegated from the Barclays Premier League to the Championship last season, expired.
The Welsh club would like the 31-year-old to stay and have made him an offer. But Rangers have also expressed an interest in signing him.
Elsewhere, McGregor, whose contract with St Mirren has just run out, is keen to join the Championship club.
Rangers chief executive Graham Wallace stated this week, despite no announcement being made on how many season tickets had been sold, that there will be more signings.