The Red Devils are set for a massive transfer window later this year, with David Moyes believed to have a budget of over £100m to rebuild his struggling squad.
A number of big name stars have already been linked with switches to Old Trafford, and now Lallana and Shaw have emerged as the latest two.
The Saints duo have both been in excellent form this term, with their fine displays having earned them spots in the England national side and prompted talk of World Cup call-ups.
This has alerted Moyes, who sees the players as possible additions.
Shaw has been a target for United for some time, with the flying left-back being hailed as a long-term successor to Patrice Evra – who may leave the club when the season ends.
Chelsea are also keen, but Southampton are believed to be unwilling to sell their £20m-rated teenager.
Lallana is also thought to be seen as a player to turn around the Premier League champions’ ailing fortunes.
The creative attacking midfielder is being viewed as a possible signing with the likes of Shinji Kagawa, Nani and Ashley Young all rumoured to be available for a transfer.