But is now the time to strike for Celtic boss Brendan Rodgers?
The Republic of Ireland winger is a well-known Celtic fan who claimed to the club's official website last month that it's his "dream" to one day pull on a Hoops shirt.
The Clarets are doing very well in the Premier League but you wonder whether the 28-year-old would find it hard to turn down the Scottish Premiership champions if they came knocking - and circumstance suggests that they should.
Rodgers has lost Patrick Roberts and Jonny Hayes to long-term injury, meaning that Scott Sinclair and James Forrest are the Northern Irishman's only fit wingers at the moment.
And a player of McClean's talent and experience would certainly fill the void left by those two.
But the longer Rodgers waits, the more of an opportunity Burnley boss Sean Dyche has and the Celtic manager needs to act fast.
McClean has been waiting on the Celtic call for his entire senior career, but there will be a limit to his patience and surely Rodgers knows that time is of the essence as Burnley loom.