The 22-year-old forward has been in impressive form for the Swans so far this campaign, and has alerted the attention of a number of rival Barclays Premier League clubs.
Sinclair would be seen as an ideal signing because he can play wide on either flank, as well as through the middle.
With Luis Suarez ruled out of action until mid-February, and fellow striker Andy Carroll struggling to rediscover the form that prompted Liverpool to pay £35million for the former Newcastle striker last January, Dalglish is expected to step up his interest in Sinclair.
However, Dalglish insists he is happy with Carroll's effort and application since arriving on Merseyside, and stressed that the striker is doing a lot of work that goes unnoticed, which proves his commitment to the team ethos.
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