Murphy is currently about to enter a 16th season with the East Midlands club having moved to England as a teenage trialist back in 1997.
The Irish full back has notched up over 300 appearances for his club - tasting Heineken Cup, English Premiership and Anglo-Welsh Cup glory along the way - and won 72 caps for his country.
And while so many of his club colleagues from the majority of his Leicester days have called time on their illustrious careers already, Murphy has the chance to push on past the next Lions tour if he continues to impress this term.
"We hope Geordy has a big season for us and his future here will be down to what he does over the next 12 months," Cockerill told the Leicester Mercury.
"He still loves playing and he is in good nick. And now he is not away with Ireland on Test duty (after last season's retirement from international rugby), we can manage his workload in-house.
"We will see where he is at when a decision needs to be made. If he has a good season and wants to carry on, then he might get the opportunity. It will all depend on what he wants to do and how well he is playing.
"If he stops playing for us like Lewis Moody, Martin Corry and Ben Kay have done in the last few years, we will just have to manage that the best way we can do."