The PA news agency has reported it understands the Giants have at least five positive cases which would be enough to force them to close down training and edge them towards calling off the Round Nine fixture at the John Smith's Stadium.
A decision is expected to be made later this afternoon.
Super League has done well so far not to have any games called off because of the pandemic.
The 2020 campaign was blighted by outbreaks at numerous clubs which caused havoc with the fixture list and prompted the Rugby Football League to rule that league positions will be determined by win percentages.
They have gone with that method again this term and, if Friday's game is called off, that will vindicate their decision.
The Championship match between Halifax and Sheffield Eagles in May was postponed after two Eagles players returned positive tests and five more were forced to isolate under track and trace regulations.
Sunday's Women's Super League derby between St Helens and Wigan has been called off after a Saints players tested positive in the wake of Saturday's Challenge Cup final victory over York and more than five of her team-mates were ordered to self-isolate for 10 days.