The club are also understood to be delighted with his decision, knowing that with only three or four years left at the top of the game, the move to Madrid presented him with perhaps his last chance of a lucrative transfer before the end of his career.
Reports in Spain, however, indicated that Real Madrid broke off negotiations with Arsenal late last night following a row over a sudden increase in the fee demanded by the Gunners.
Spanish newspaper As reported that Arsenal's demands for the player had risen sharply from £22m to £25m yesterday.
There has also been speculation that Vieira and Real Madrid could not reach agreement over his personal terms.
It is understood Vieira was demanding the same money as the club's existing crop of "Galacticos" such as David Beckham, Zinedine Zidane and Raul.
As recently as last night Wenger spoke of his fears that his talismanic leader had played his last game for the club.
He said: "I wouldn't say I am genuinely optimistic Patrick will stay. But the deal with Real isn't done and if it's not done by this weekend then he is staying at Arsenal."
Vieira is expected to miss Arsenal's opening Premiership clash against Everton on Sunday through a thigh injury.
