Salah has enjoyed a remarkable season since joining Liverpool from Roma last summer and notched four goals in last weekend’s 5-0 win over Watford.
His tally of 35 goals for the campaign in all competition has left him in sight of the 42 Cristiano Ronaldo scored in his penultimate season at Manchester United.
Liverpool fans across the globe will be hopeful Salah’s strikes do not lead to him following in Ronaldo’s footsteps by leaving the Premier League for Real.
And Keown admits he does not want Liverpool to lose the 25-year-old to Real or their El Clasico rivals Barcelona.
"Salah has hit the best form of his career," Keown told the Daily Mail.
"Earlier in the season it struck me how many chances he missed but he has become more ruthless as the season has gone on.
"The challenge for him is to continue this form into next season.
"I just hope that the adulation from the Anfield fans, the buzz from scoring and winning is enough to prevent him from wanting to join a Real Madrid or a Barcelona."
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Mohamed Salah has been tipped to leave Liverpool for Real Madrid or Barcelona in the summer
Mo Salah is Premier League's Player of the Year says Burley
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Mohamed Salah has scored 35 goals for Liverpool in all competitions this season
Keown’s comments came after he was asked whether Salah or Manchester City’s Kevin De Bruyne was his player of the year.
"Football at the highest level is artistic and I’ve said before that De Bruyne’s feet are like paintbrushes," he said.
"He is a special, special talent and my player of the year."
Salah and De Bruyne will go head-to-head when Liverpool take on City in the Champions League quarter-finals next month.