However, the Daily Record report that that Davis is keen to continue his playing career, with the Nothern Ireland international now "close to agreeing" a new one year deal with the Scottish Cup winners.
Discussing his future after the 2-0 win over Hearts at Hampden earlier this month, Davis said: "To be honest I really don't know.
"I think we just said we'd speak after this.
"It's been such an emotional week obviously with the European cup final - this doesn't make up for it because it was a real good opportunity for us but we're delighted to win this - then Jimmy Bell's funeral yesterday.
"It has been a really emotional week and I'm delighted we could finish on a high.
"We'll sit down next week or so and see where everything sits."