Aston Villa had been expected to complete an £8million loan deal for the England midfielder but Cleverley is now believed to prefer a reunion with Roberto Martinez, who he played under at Wigan Athletic in 2010-11.
Paul Lambert had been hopeful of securing an £8m deal for Cleverley but his £60,000-a-week wage demands have proved to be restrictive; Hull City are also interested although Cleverley does not see them as an attractive option, according to reports.
Video: Transfer deadline day
Everton are now at evens with bwin to sign Cleverely, though there are no rumours surfacing from the club that they are interested having spent almost £40m on Romelu Lukaku, Gareth Barry, Muhamed Besic and Samuel Eto'o this summer.
The 25-year-old is among a number of players told by Louis van Gaal that he can leave Old Trafford, though Clevereley may see out the final year of his contract, knowing he can leave on a free next summer.
Martinez took Cleverley to the DW Stadium in 2010, playing him in 25 Premier League matches in an impressive loan spell where the midfielder added four goals.
On his return to Manchester United, Sir Alex Ferguson handed Cleverley his United debut.