Lambert is believed to be considering whether to firm up his interest in the 23-year-old, who has impressed the former Norwich manager.
Lowton, who has two years remaining of his current contract, has made nearly 100 appearances for the Blades since making his first team debut during the 2009-2010 campaign.
United boss Danny Wilson admitted some players may reconsider their futures after losing the League One play-off final to Huddersfield.
Championship sides Ipswich and Derby have been linked with a move for Lowton who also had a spell on loan at Hungarian club Ferencvaros.
Lambert successfully brought several players through the lower leagues at Carrow Road and Lowton is the type of player he likes to work with.
Alan Hutton was Villa's first choice right-back last season after his £3million move from Tottenham. But the Scotland international struggled to show his best form and Eric Lichaj impressed when given the chance to replace him by the then Villa manager Alex McLeish.
Lambert is keen to increase competition for places at the back after strengthening the midfield department with the signing of Karim El Ahmadi from Feyenoord.
Villa reported back for pre-season training on Thursday and the squad met Lambert for the first time since his appointment last month.
Central defender Richard Dunne and goalkeeper Shay Given have been given extra time off after appearing for the Republic of Ireland during Euro 2012.
Source: PA
Source: PA