The highest bid was £2 million for the 19-year-old midfielder who is the Scottish Football Writers’ Young Player of the Year.
Motherwell, however, are holding out for a £3m package for their academy graduate. Both clubs are believed to still be talking with the Fir Park outfit.
Responding previously to speculation, Fir Park chief executive Alan Burrows stressed that any potential suitors for Turnbull will have to come up with a fee in excess of the record £1.75m they received in 1994 when Phil O’Donnell moved to Celtic Park.
Turnbull scored 15 goals in 30 league appearances for the Lanarkshire side last season and was rewarded with a new deal, tying him to the club until the summer of 2021.