The American takes on Tszyu on March 12 after the Sydney boxer's original opponent Jermell Charlo (32), who holds the WBO, WBC, IBF and WBA belts, broke his hand in training in December.
Harrison is hoping to set up another fight against compatriot Charlo, having beaten him for the WBC belt in 2018 only to lose the rematch the following year.
He remains the only boxer to have beaten Charlo.
"It's everything for me, man," Harrison told a media conference from Detroit on Wednesday.
"He's chasing the same thing I'm chasing. The same man he's looking for is the same man I've been looking for.
"So I swear I'm really hugging Tim right now because without Tim there was no other possible way that I was ever going to possibly get the opportunity to get back to the fight I want.
"For him to say yes to a guy like me, he woke me up out of the dead. This is me hugging you, Tim.
"You brought me back to life."
Tszyu could risk his hope of a unification bout against Charlo with defeat to Harrison, a point not lost on the American.
"We need to talk to management because, like, for him to be at the doorstep for all the marbles and to accept a fight with the only man that's beat the man that you were looking to beat, we need to talk to management about this one," he said.
"We need to go to HR. Something ain't right about this one."
Tszyu, the son of former undisputed light-welterweight world champion Kostya, is undefeated in 21 fights but was derided as "basic" last week by Harrison.
"No hugs and kisses from me," said the 28-year-old.
"This is the name that I need ... to wake all these boys up.
"I came in to the sport not to just muck around but to really take over."
