United boss David Moyes is keen to strengthen his midfield options in the New Year and has now been tipped to make a move for Lallana.
The Saints star has been in impressive form this season and made his England debut in November.
It has been speculated that United could launch a January move for Lallana, with a £15million fee mooted, but Southampton boss Mauricio Pochettino has stressed on a number of occasions that he is under no pressure to sell.
The 25-year-old is also desperate to be included in England's World Cup squad and may snub a mid-season move in order to ensure he is guaranteed first-team football in the remainder of the campaign to give himself the best possible chance of making the final 23-man squad.
United have also been linked with Atletico Madrid star Koke and Brazilian midfielder Everton Ribeiro, who currently plays for Cruzeiro, as Moyes seeks to bolster his midfield ranks in January.