Burnley striker Jay Rodriguez is set for a Southampton medical.
The Lancashire Telegraph says Rodriguez will not be rushed into a decision over his future.
The Burnley striker will go straight from the airport to meet with the Premier League newcomers for the first time, following his return from holiday.
But contrary to reports the south coast club will not demand an immediate answer to their offer, even though they are already playing a patient waiting game.
Fulham had an earlier £5m bid rejected, while there have been enquiries from a number of other top flight teams, including Newcastle United, West Ham and Aston Villa, as well as Championship side Cardiff City, who are being backed by billionaire Malaysian owner Vincent Tan.