After missing the start of the season through injury, Hause has been restricted to just one appearance by head coach Nuno Espirito Santo, which came in the EFL Cup defeat to Manchester City in October.
With Wolves continuing to dominate the Championship, opportunities for the 22-year-old could be few and far between and according to The Sun, the Terriers and the Hornets are monitoring the situation.
Both clubs sit comfortably in mid-table in the Premier League but only Stoke City and West Ham United have conceded more goals in the top flight.
While Hause - who can also play at left-back - is short of match practice, he could be available for just £2.5m while the player would also count as a home-grown talent in either Huddersfield's or Watford's 25-man squad.
Hause currently has 18 months remaining on his contract at Molineux.