The Scot is believed to be in the market for defensive reinforcements this summer, with long-term enforcers Nemanja Vidic – who is certain to leave to join Inter Milan – and Rio Ferdinand set to be phased out.
Moyes already has Phil Jones and Chris Smalling to step in, but with the duo inexperienced he is looking at drafting in a commanding presence.
Lovren is thought to have caught his eye after a wonderful debut season in the Premier league with Southampton.
The 24-year-old has been a key member of the Saints’ impressive rearguard – which has been breached on only 37 occasions in 30 games – forming a strong partnership with Jose Fonte.
Although Luke Shaw is rumoured to be United’s top target based at St Mary’s Stadium, the Croatia international is seen as a top potential addition.
The South Coast club are unlikely to entertain the notion of selling their man, but the player himself is believed to be open to a big move.