The Times reports that Liverpool's extraordinary offer comes just six months after Johnson was valued at £8.5 million.
The England international has since signed a four-year contract extension, and interest from Chelsea and Manchester City appears to have sent his value skywards.
Álvaro Arbeloa and Andrea Dossena will reportedly be sold to finance the move for Johnson, who will hope to cement his place in England's World Cup back four by moving to a Champions League side.
Portsmouth still owe Liverpool money from Peter Crouch's transfer last summer, and those payments will be included in the Johnson deal.
Johnson, now 24, was one of Roman Abramovich's first signings when he joined Chelsea from West Ham as a teenager.
Having failed to establish himself in the first team at Stamford Bridge, he was signed by Harry Redknapp at Portsmouth, where he was matured off the pitch, and developed into a highly accomplished attacking full-back on it.