The Gers are on the lookout for a new head coach following the departure of Steven Gerrard to Aston Villa on Thursday.
Koeman was sacked by La Liga giants Barcelona at the end of October, after a challenging 14 months at Camp Nou, and is now considering a swift return to management.
The report goes as far to say that Koeman is the favourite to take the Rangers hotseat and claim that the Dutchman's next destination will be in Scotland with the Premiership champions.
Meanwhile, fellow Dutchman Giovanni van Bronckhorst, who remains the favourite with the bookmakers, is understood to have met with the Rangers hierarchy in London on Saturday and held initial talks over the current vacancy.
Koeman has managed a total of 749 matches with 11 different teams across a 21-year coaching career and has won nine major pieces of silverware. body check tags ::