Saints have a deal in place to sign Stewart from Sunderland for £8m plus a further £2m in add-ons.
He has travelled to the south coast to undergo a medical check, with Southampton likely to want to be very thorough given the fact he has been nursing an injury.
It has been claimed in some quarters that Stewart has failed his medical at Southampton.
Those claims are wide of the mark though.
Stewart has passed every medical test he has so far taken with the Saints.
He still has the final part of his medical to complete, but the move from Sunderland to Southampton remains very much on course to happen.
Southampton are aware that Stewart has been out injured and still chose to slap in a bid with Sunderland to sign him.
All eyes will be on whether they do eventually slide a contract under the striker’s nose to sign.