
The winger, a sub in England's midweek draw with the Czechs, believes his ambitions will be aided by a move to a Champions League club.
Rafa Benitez has been considering an offer all summer, but with his focus on the Gareth Barry saga, Downing's hopes of a transfer appeared increasingly unlikely.
The Anfield boss has also been in talks with Espanyol for Albert Riera, having given up on Valencia's David Silva.
Now Rafa is ready to make a last-ditch attempt to solve his left-sided problems - with both Riera and Downing on his agenda.
Riera is valued at £10m by Reds but Everton have bid £12m for the ex-Manchester City midfielder.
That may force Benitez to move for Downing, who may cost £16m.