The Chilean ended his first season in England with two pieces of silverware after City added their second top-flight crown in three years to the Capital One Cup they claimed back in March.
The Reds recorded a 2-1 final day victory over Newcastle but defeat against Chelsea and draw with Crystal Palace damaged their title aspirations.
Shaw has been widely mooted as an Old Trafford target this summer and it appears they are keen to get their business done before the World Cup and before they have appointed a permanent manager.
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