The Saints duo have been two of the Premier League’s most exciting talents this term, helping the South Coast club to a solid midtable position.
Their impressive displays have caught the eye of Moyes, who is ready to pay in excess of £35m for the pair.
Shaw is thought to be the top target, with the 18-year-old left-back seen as an ideal long-term replacement for Patrice Evra.
The teenage ace has already established himself as a key first-team player at St Mary’s Stadium, and is even being tipped to break into the England squad for the World Cup after making his debut.
Lallana on the other hand is expected to be on the plane to Brazil on the back of a terrific campaign.
United are also keen to lure him to Old Trafford in a bid to inject some more creativity into their attacking midfield.
The Hampshire club are far from keen to sell either of their stars, but offers of £20m for Shaw and £15m-£20m for Lallana may prove too good to turn down.
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