The Red Devils were linked with the impressive England international over the summer, but elected against pushing a deal.
Clyne has since continued to impress on the South Coast, with his bombarding displays down the right flank having been key in the Saints’ top four push.
But with the 23-year-old now in the last 18 months of his contract, Southampton face a dilemma.
The Hampshire outfit are desperate to avoid losing another star name after the summer ‘exodus’, but they’re aware that Clyne’s value will decrease significantly if they cannot tie him down to a new deal before the summer – which they’re understood to be trying to do.
This has alerted Van Gaal, who is keen to add a more reliable right-sided defender to his squad with Rafael and Antonio Valencia yet to convince him of their abilities.
Liverpool are also monitoring the situation.