The Celtic defender is keen to leave Celtic Park for a move south of the border, with Saints said to have beaten off competition from rival clubs to land the ace.
Southampton are thought to have agreed an £11.5million deal for the 24-year-old.
And, despite Celtic's hope of retaining the Dutchman, it appears a permanent transfer will go ahead before the Premier League's 6pm deadline.
The Hoops agreed a £4m fee with Dinamo Zagreb for 21-year-old Simunovic last night and he is now awaiting clearance on a UK work visa.
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Ryan Christie is set to join Celtic today
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Meanwhile, Christie's £500,000 move from Inverness will be concluded this afternoon.
The 20-year-old will, however, be loaned back to the Highlanders for the remainder of the season should a deal go through.