Villa, who are looking for a new forward to bolster their underperforming front line, are believed to have offered €6million for the England international.
Lambert, 32, has struggled to make an impact since joining his boyhood club last summer but does not appear prepared to give up his Anfield career for Villa Park. The Reds brought in
Lambert, who travelled to the World Cup with England last year, for €5m from Southampton as they reshaped their squad following the sale of talisman Luis Suarez.
He scored 14 times for Saints last season but has failed to replicate that form for Liverpool, scoring just three times this term, including one against Villa last month.
His situation had led to speculation he could move in the winter transfer window and that was fuelled further by the successful return to action of Daniel Sturridge at the weekend after five months out.
Manager Brendan Rodgers had indicated that he wanted the player to stay but the club do not appear to have stood in his way following Villa’s enquiry.
The player’s decision to reject the move suggests that Lambert intends to remain and fight for a place along with the likes of Mario Balotelli and Fabio Borini.
Villa’s interest in Lambert is understandable given their poor form in front of goal in the Barclays Premier League. Paul Lambert’s side have scored just 11 goals in 23 games.