Bjornebye is a former Reds fullback and said on Egyptian channel Modern MTI's Modern Sports discussion programme that Salah's name has been raised at Ibrox.
Bjornebye said: "I don’t know what Mo's plans are - we discussed it at work today as well, as I’m an advisor to Rangers.
"We discussed where he’ll go and so on. But I think most people are grateful for what he’s done for Liverpool.
"He is a true legend at Liverpool and has achieved a remarkable legacy for a great club. He has delivered exceptional results for them over many seasons.
"There were some heated discussions about his situation last year, but the matter has been resolved and he has remained loyal to Liverpool.
“I think most people can accept that he has given the club many great years and now wants to seize a new opportunity, perhaps embarking on another adventure."