Scarlets head coach Wayne Pivac says he would welcome Jonathan Davies back to the region but has not spoken to the Wales centre about a possible return.
Davies is due to play for his French club Clermont-Auvergne next month after recovering from the knee injury that ruled him out of the World Cup.
The 27-year-old left Scarlets for Clermont in 2014 but reports in France suggest he will leave the Top 14 side.
"If he were to become available we'd enjoy having him back," Pivac said.
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The British and Irish Lions centre joined Clermont Auvergne on a two-year contract ahead of the 2014-15 season.
Davies was part of the Clermont side that lost to Toulon in the Champions Cup final at Twickenham in May 2015.
But a few weeks later Davies suffered a ruptured and anterior cruciate ligament injury which ended his World Cup hopes.
The centre's stay in France has been hindered by injury, and reports suggest Clermont may be ready to release him before his contract expires at the end of the season.
"I'll make it quite clear," added Pivac. "Any Scarlets players that have left the region and, for whatever reason, when they are available then we would certainly want to talk to them and see if there form is good enough to come back.
"Under the rules we'd have first crack at signing Davies and if the opportunity came up to play here again no doubt we would welcome him back with open arms."