Black Cats manager Steve Bruce is believed to be resigned to losing the England Under-21 midfielder to Anfield, but will use any revenue raised from a deal to finance the signings of Crouch, as well as Manchester United's Wes Brown and Darron Gibson.
Bruce is currently abroad and Henderson travels today to Denmark for the European Under-21 Championship, and any tentative enquiries will only be made official at least once Bruce returns from his holiday.
Bringing Crouch to Wearside will end a lengthy pursuit of the 6ft 7ins Tottenham forward. Bruce tried to sign Crouch two years ago, but opted to go to White Hart Lane, while Roy Keane failed to tempt the beanpole striker to the Stadium of Light in 2008 while a Liverpool player.
Crouch scored 12 goals in 47 appearances for Tottenham, including a hat-trick against Young Boys in the Champions League, but Harry Redknapp is prepared to listen to offers.
Meanwhile, Sunderland reserve boss Keith Bertschin expects midfielder Jack Colback to play a bigger part in the first-team next season.
The 21-year-old was used regularly at the end of the season as Sunderland struggled with injuries to ten first-team players.
But despite the expected returns of Lee Cattermole, David Meyler and Kieran Richardson, Bertschin believes that Colback - who spent a portion of the season on loan in the Championship at Ipswich Town - can be a key player for the Black Cats.
"Jack's a quiet lad and lets his deeds do the talking. He's one who leads by example," Bertschin told the club's official website yesterday.
"Jack has made a real case for himself in the first team. Remember, he came into the team in a difficult situation.
"He came in where the team weren't winning, there wasn't a lot of confidence, the pressure was on and it was hard work.
"But he has been brilliant. Jack has proved he can stay in the team on merit."
Colback started against Birmingham in April and kept his place in the team for the remaining Premier League fixtures, excelling in Sunderland's 2-1 victory against Bolton.
And Bertschin paid tribute to Killingworth-born Colback's mentality.
"Jack's a dedicated boy and that's huge for a professional footballer," he said.
"When your job really depends upon fitness there is a certain amount of sacrifice involved.
"You have to really get the right sleep, eat the right food and train as hard as you can.
"Young players can't have as much social time as their friends and that's the price they have to pay.
"I've been hugely pleased with Jack because he's grabbed his chance. As coaches we can only give players so much help - eventually they have to help themselves."
Sunderland's Asamoah Gyan was on the scoresheet as his Ghana side lost to South Korea in an international friendly yesterday.
A last-minute goal from Koo Ja-cheol gave the Koreans the win after Gyan had cancelled out Ji Dong-won's opener.
Gyan missed a penalty after being brought down by Hong Jeong-ho.
Crouch, meanwhile, will consider his England future over the summer after admitting his disappointment at being left out of the matchday squad for last Saturday's Euro 2012 draw with Switzerland.
Despite being joint-16th on the list of England's all-time top scorers, England manager Fabio Capello opted against including Crouch on the bench at Wembley.