Rated as a potential rising star in the Premiership, the versatile back made five appearances for Carnegie, having arrived for their Championship Cup campaign last month.
Umaga, 20, played three games at full-back but also featured at inside centre and fly-half.
Carnegie director of rugby Chris Stirling was impressed and explained about the situation, saying: “He’s gone back to Wasps to now play some A League rugby but I’m hoping he’ll be back here.
“There’s a chance Jacob could return in time for our next Championship match at Doncaster Knights on December 29 and then stay for the rest of the season.
“It’s a deal that’s still in discussions; we’re in the process of talking to Wasps about it.”
It would be a major boost to Carnegie’s hopes of pulling away from the bottom of the Championship if they can retain the services of the Halifax-born player and son of former Rotherham Titans star Mike Umaga.
It remains to be seen which is his best position but Stirling said: “For us, at the moment, he’s a 15 (full-back).
“That said, when he played down at Doncaster at 12 (centre) he was outstanding.
“He is a versatile player who can play 10, 12 or 15 but he’s being doing a good job for us at full-back.
“Although he’s not available this weekend we’ve got some great back-up in Myles Thoroughgood, who is a very tidy player out the back.
“He’ll provide us with plenty of attacking options.”
Thoroughgood has made just one appearance since arriving from New Zealand in October so he will look to make a quick impression.
Umaga, meanwhile, scored a try on debut against Nottingham and kicked 50 points during his initial stint, Carnegie winning four of their five Cup games.
Stirling’s side have, then, already qualified for the quarter-finals – as have today’s in-form visitors Coventry – ahead of this afternoon’s final pool fixture.
Coventry inflicted Carnegie’s only competition defeat so far with a 51-32 victory last month and know if they can repeat that result they will usurp their rivals from the top of the pool.
Whoever finishes first will be guaranteed a home quarter-final.
Stirling said: “We want to keep building towards that Doncaster game.
“The Championship Cup has been great for us and come at just the right time to help bed in our new signings and find some form.
“Coventry are going well and it will be another tough match although no tougher than the ones we’ve already faced against Doncaster and Nottingham in recent weeks.”
Will Britton and Sam Nixon have also returned to Bath Rugby while Harry Davey replaces Chris Elder on the wing as Carnegie seek a fourth straight win.
Up front, Matt Smith returns from injury, Andy Foster comes in for Jake Ilnicki, who is on the bench, Josh Bainbridge starts instead of Cian Romaine and Tom Hill joins the replacements.