The Sun reports that Chelsea and Manchester City are on red alert and could make a move for Villa.
Manchester United, Barcelona and Real Madrid are also keen on the highly-rated Spain international.
Valencia are hoping the sales of Villa and team-mate David Silva could bring in £50million in the summer.
Villa said: “For now my head is in Valencia and the World Cup.
“After South Africa I will decide what’s best. My final decision won’t be based solely on money.”