The club had agreed a fee of £8million with Manchester United but the England international priced himself out of a move.
Cleverley is believed to have asked for £60,000-a-week and Villa ended their interest on Monday when it became clear negotiations had reached an impasse.
Hull were interested but Steve Bruce instead made a late move for Newcastle's Hatem Ben Arfa.
Cleverley had been made available by Old Trafford boss Louis van Gaal and looks to have no future at United.
He was a long-term admirer of Tottenham's Lewis Holtby but the midfielder joined Hamburg on loan.
Yet the cash Villa were prepared to spend on Cleverley represented a massive show of faith from chairman Randy Lerner.
The American is looking to sell and Lambert has previously been restricted to free transfers and bargain buys.
Villa signed Joe Cole and Philippe Senderos on free transfers earlier in the summer while also snapping up Kieran Richardson for around £600,000 from Fulham and Carlos Sanchez for an undisclosed fee from Elche.
The club also cleared out some of last season's purchases with Aleksandar Tonev, Nicklas Helenius and Antonio Luna all leaving on loan.
Villa had earlier sold midfielder Karim El Ahmadi back to Feyenoord for an undisclosed fee on Monday.
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