The 23-year old has performed at a high level for the Saints this season and his current manager expects plenty of enquiries for him this summer.
"There has been no contact from any club," St Johnstone boss Derek McInnes told the Daily Record.
"But do I expect interest to firm up in Murray? The answer would have to be yes."
Davidson joined the Saints from Livingston in 2009 and has appeared about 60 times in the league since his shift. He has also represented Scotland at U21 level and was on the bench for the recent senior international friendly with Brazil in London.