The Manchester United boss is desperate to land a long-term replacement for Patrice Evra in theJanuary transfer window.
Evra is expected to leave Old Trafford in the summer so he can finish his career in France.
The defender, 32, has been offered a multi-million pound deal to join Monaco, while Marseille and Paris Saint Germain are also keeping close tabs on him. His departure will leave Moyes with a huge void to fill and the United boss has identified Leighton Baines and Luke Shaw as his top targets to replace him.
Starsport understands Evra will not rock the boat if Moyes signs a new left-back.
But Moyes is convinced former club Everton will not sell Baines in the January transfer window.
He tried to land the England defender in the summer but the Toffees dug their heels in.
And he fears they will do the same again with them pressing for a Champions League place.
Moyes is worried Southampton will do the same with rising star Shaw and reckons the Saints will refuse to sell the England Under-21 star, even if he meets their £10m valuation.
It is understood United have enquired about Shaw in detail and have even studied his training methods and diet with a view to making a bid.
But Saints are challenging for Europe this season and Shaw is crucial to their hopes of success.
Meanwhile, Evra reckons United have got their title-winning hunger back.
“We have that winning mentality and United spirit which was missing at the start of the season,” he said.
