Both players are currently due to return to St Mary's when their loan contracts expire on June 30, but the 2019-20 season may not be over by then due to the lockdown in place amid the coronavirus outbreak.
Football in England has been suspended until the end of April at the earliest, although there are fears that the postponement of the campaign could stretch further beyond that.
The unprecedented situation has cast uncertainty over the futures of players whose contracts expire this summer - including loanees - but talkSPORT claims that Southampton are not worried about the on-loan pair.
The Saints would reportedly be happy for both players to extend their stays with Neil Lennon's side, who are well on course for a record-equalling ninth successive Premiership title.
Elyounoussi has been something of a bit-part player at Parkhead, making only 20 appearances this season, but Forster has been a key member of the Celtic first team. body check tags ::