They are also bracing themselves for the possibility that top goalscorer Kevin Nisbet could be heading in the opposite direction.
The Easter Road club are aware that Nisbet, who they signed from Dunfermline last July, is on a Celtic Park watchlist. But, with no manager yet in place, following the breakdown in talks with Eddie Howe, there have been no solid approaches for the 24 year-old forward.
After rejecting bids from Birmingham City in the January window, Hibs do not expect to get through the summer without further approaches, especially if Nisbet can make his mark with Steve Clarke’s Scotland squad at the upcoming Euros.
Which is why they are already eyeing up attacking reinforcements, with Griffiths one of those they are chasing.
The 30 year-old was omitted from the Scotland set-up despite scoring one of the penalties in the spot-kick shoot-out victory over Serbia in November. That result saw the country qualify for a major finals for the first time since 1998 but with fitness problems and personal issues blighting his season, he has scored just twice since Christmas.
His current deal with the Glasgow giants, who he joined from Wolves at the beginning of 2014, is due to expire today and while the club has an option to extend that by a year, there has still been no word on whether they will choose to activate that and retain the services of the 30 year-old who has scored 123 goals and won seven Premiership titles, three Scottish Cups and four League Cups in his eight seasons at Parkhead.
If they choose not to, Hibs are poised to make a move for the player who has already enjoyed two prolific loan spells at his boyhood club, netting 11 goals throughout the 2011/12 season before banging in a further 28 goals the following year.
With European football to look forward to next term, along with the task of maintaining their place in the Premiership top three and bettering the semi-final and final finishes in the cup competitions, an early signing would give them some peace of mind if Nisbet’s suitors do come calling.