The Spaniard has pulled ahead of Chelsea in the race to sign the Portsmouth player after both sides had bids accepted by the south coast club over the weekend, while Manchester City are believed to have made a firm inquiry.
Johnson is thought to have made his preference for a move to Anfield clear after Portsmouth admitted they would not stand in his way if he wished to leave the club for Champions League football.
Two Liverpool bids, in the region of £12 million, were turned down by Portsmouth last summer and in January but Benitez is confident a £10 million fee paid over two years, plus an agreement to write off the £7 million the south coast club still owe for Peter Crouch, will be enough to land the former Chelsea player.
Benitez may sacrifice two full-backs to ensure he has the funds to bolster his attack as well, with Andrea Dossena edging closer to a £6 million move to Juventus.
Alvaro Arbeloa, the player Johnson would directly replace, could also be sold, with the Liverpool manager braced for an £8 million approach from Real Madrid once Spain's involvement in the Confederations Cup ends.
Arbeloa has just 12 months left on his contract and, while Benitez had suggested he would be offered a new deal, his failure to sign one indicates his time on Merseyside is drawing to a close.
Benitez may yet, though, be able to fend off Real's interest in playmaker Xabi Alonso. Florentino Perez, the new Madrid president, has suggested he would make an offer for the Basque but his sporting director, Jorge Valdano, said yesterday: "Liverpool have issued an official public statement and Xabi is a player who has little chance of joining Real Madrid.
"They valued him at £16 million last season because he was not an essential player, but he is now. They've given him more chances to play and he has responded magnificently."