The England striker, 29, has been linked to Premiership runners up Arsenal but left for France today with the rest of the England squad without stating his intentions.
Leicester will be due a substantial compensation payment if the former Fleetwood Town forward leaves as he signed a new three-year contract with the Premier League champions in February.
Golf: Scottish Open organisers expressed disappointment that defending champion Ricky Fowler will not defend the title at Castle Stuart.
The world number five says a busy calendar, including the Olympics, means he cannot squeeze the tournament into his schedule.
Tournament director Peter Adams said he regretted the absence of Fowler.
“No Ricky this year, which we’re obviously disappointed about and so is Ricky,” Adams told BBC Scotland.
“He has written to us and said he would have really liked to come back to defend, but it is some of the schedule congestion that has been an issue for him.”
Adams said the golf calendar was “incredibly congested” and players have some difficulty organising their schedules.
The 27-year-old won his Scottish Open title at Gullane, but the tournament returns to Castle Stuart from 7 to 10 July after an absence of three years.
Ian Poulter has been named one of Europe’s vice-captains for the Ryder Cup.
The 40-year-old Englishman is ruled out of the tournament because of arthritic problems in his right foot which will prevent him playing for four months.
Poulter said he was “truly honoured” to join Thomas Bjorn, Paul Lawrie and Padraig Harrington as vice-captains to skipper Darren Clarke.
This year’s Ryder Cup takes place at Hazeltine National in Minnesota from 30 September to 2 October.