The Holland star has made it clear his preference would be to rejoin Ajax but they have shown little interest in taking him as they push for £25million in straight cash from Liverpool for Luis Suarez.
Hoffenheim have now offered £7m, rising to £8m on performances and a deal worth £70,000 a week for the 24-year-old.
Enlarge Enlarge Revolving door: Babel looks to be heading for the exit but will Suarez replace him?
The Anfield club accepted Hoffenheim's offer last week but the player had returned to Liverpool, where he resumed training.
Personal terms have now been settled, though, and a Liverpool statement last night read: 'Ryan Babel has agreed a move to Hoffenheim. The Dutch international will fly to Germany to finalise the deal.
'The move comes six days after Liverpool accepted a bid for the 24-year-old striker.'
Sunderland and Fulham will be disappointed as both strive to find suitable strikers. Sunderland were also rebuffed in a £3m offer for West Ham's Frederic Piquionne on Monday and continue to negotiate over Stoke's Ricardo Fuller.
Liverpool, meanwhile, are considering their options after talks over Suarez stalled and Babel could still figure in negotiations if the Hoffenheim deal collapses.
Damien Comolli, Liverpool's director of football strategy, held a brief meeting in Amsterdam with Ajax general director Rik van den Boog, who told him the Dutch club would not consider an offer below £25m for Suarez. Ajax claim Liverpool have offered only £12.7m.
An Ajax spokesman said: 'We'll have to wait for them to come back with something more respectful. If you compare the £12.7m Liverpool want to pay for Suarez with other transfers you can imagine that it's far too low for us.' Charlie can be your boy for £14m! Ollie tells Reds to 'put up or shut up' in quest for Adam Liverpool move for Suarez stalls as Ajax refuse to budge on £25m feeWhy didn't you attack Dalglish? Angry Houllier hits out at Holloway over AdamAll the latest Liverpool news, features and opinion
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