Harrison has not featured since being forced off inside the opening 10 minutes of the semi-final clash with Newcastle Falcons at Franklin's Gardens on February 9.
The No.8 has been battling to overcome a hamstring problem, but he returned to training last week.
And Harrison now looks set to be available play in this weekend's sell-out game at the Gardens.
"Teimana trained the back end of last week, he's trained at the start of this week and he's looking good," confirmed Saints defence coach Alan Dickens.
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James Haskell is also fit to play after recovering from a toe injury.
"He's training in and out, managing that so he's available," Dickens said.
And Ehren Painter, who has had a calf problem, could also be up for selection.
"He did his injury in training a couple of weeks ago but he's on the way back as well," Dickens said.
Saints face a slight shortage in the second row after injuries to Courtney Lawes and David Ribbans.
Dom Barrow recently left the club, meaning the likes of Api Ratuniyarawa, Alex Moon, Alex Coles and fit-again James Craig will be asked to share the workload.
Coles will play for England Under-20s against Scotland Under-20s at Franklin's Gardens on Friday night, meaning Ratuniyarawa, Moon and Craig are likely to feature against Saracens.
Craig returned from injury last weekend, coming off the bench during the defeat to Bristol Bears.
And Dickens said: "James is a player who has had a lot of experience here.
"He's been unlucky through injuries during the past three or four seasons but we know he can come in and slot into the squad.
"He can slot into the starting team and put in a good performance.
"It's unfortunate he's picked up those knocks when he's been kicking on.
"He's certainly a talented player and he will always do his best."
Andy Symons, Mike Haywood and Harry Mallinder remain sidelined for the rest of the season.
But that does not mean the trio haven't been playing their part.
"It's tough for them, they're long-term injuries and I'm sure they go up and down in terms of how they're feeling and where they're at," Dickens said.
"The medical staff are excellent with them, as are the strength and conditioning department.
"Mikey as well as doing the rehab, he goes out and gets involved in unit sessions with the forwards so he's around the players.
"The others have been involved in doing analysis work so they're within the squad.
"There's no question it's tough and I'm sure they're looking forward to getting back on to the playing field."