Clarke is the Iron's top scorer this season, with 11 goals in 14 appearances, but can only feature in two more games before his loan expires.
The deal cannot be extended, meaning he must return to his parent club Charlton. He has been told he can leave The Valley in the January transfer window.
Brian Laws, the Scunthorpe boss, had feared a recall by the Addicks - allowing him to go to another club on loan until January.
But, according to BBC Radio Humberside, that will not happen as the player said he wishes to remain in North Lincolnshire for the time being.