A report The Daily Mirror claims that Liverpool have been monitoring the progress of the 27-year-old. Dalglish may be preparing a shock bid for the Northern Ireland international after other interested parties stepped up their interest.
McCourt joined Celtic in 2008 from his local club Derry City. He has made 39 appearances in those three seasons, scoring nine goals. He has failed to hold down a first-team spot with Celtic, but he is hugely talented and is highly skilled.
The signing makes sense for Dalglish. Director of Football Damien Comolli said in the wake of the Jose Enrique signing on Friday that Liverpool were done with their summer signings, but the Reds still lack depth at the wing position.
McCourt is naturally a left-winger, and behind Stewart Downing, the next best option is 16-year-old Raheem Sterling. McCourt would serve to add elite depth on the wing.
While the Reds have already spent around £65 million since the takeover of owners Fenway Sports Group, McCourt is a low-risk, high-reward option.
He wouldn't cost any more than £3 million or £4 million, but with his talent, the benefits of taking a chance on him could be sky-high.