Falcao is currently on a season-long loan at Chelsea from Monaco, a similar deal to the one which saw him play for Manchester United the year before.
But things have not gone well for the Colombian and Jose Mourinho is happy for Chelsea to cut short the deal, but there is not get-out clause in the agreement for the Blues - in that they have to pay the full £4million loan fee they agreed with Monaco - whether he goes back in January or the summer.
However, Chelsea would at least save on his six-figure-a-week salary should he find a new club, and his agent Jorge Mendes is understood to have already held talks with Valencia.
Valencia are willing to take all of his wages, but they won't pay a fee - meaning any shortfall in the deal would have to be taken on by Chelsea.
Now one of Neville's first conversations will be whether to give the green-light to the Colombian marksman, who enjoyed great success in La Liga during his two-year stint with Atletico Madrid.