The Egyptian superstar announced he is leaving the Anfield giants at the end of the season after nine years at Liverpool.
Salah, 33, will have plenty of options at the next stage of his career and a highly lucrative move to Saudi Arabia has been touted as favourite.
Former Liverpool player Bjornebye is currently a football consultant and advisor at Rangers on a six-month contract initially, although it's expected he will extend his stay.
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The former Norway international was a guest on Egyptian channel Modern MTI's Modern Sports discussion programme and was asked about the future of Salah.
And the 56-year-old revealed Salah has been discussed within Ibrox circles.
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."