The former Dundee United player would be seen as a replacement for Kris Boyd, should the out-of-contract Rugby Park talisman decide to accept an offer from elsewhere.
Goodwillie is under contract at Blackburn for another year but negotiations are under way for a compromise settlement to allow the release of the 25-year-old who joined Rovers from United in the summer of 2011 for £2m.
Goodwillie has failed to secure a first-team place and had loan spells back at Tannadice and at Blackpool.
Gary Locke, meanwhile, has agreed to become Allan Johnston's assistant at Kilmarnock. The 39-year-old, who played for the Rugby Park side between 2002 and 2009, has been without a club since being sacked by Hearts when Craig Levein and Robbie Neilson were appointed by the new Tynecastle owner Ann Budge.
Locke retains an excellent relationship with Johnston after spells playing with the Kilmarnock manager at Hearts, Kilmarnock and with Scotland Under-21s.