But any switch to The Emirates Stadium is dependent on Arsenal selling Alexis Sanchez.
The former Reds striker wrote in a column for BetVictor as he looks ahead to a crunch clash with Manchester City on Sunday: "Liverpool begin life without Philippe in what promises to be one of the games of the season played between the two most exciting sides in the division".
Mahrez is among those to have been heavily linked with a move - amid ongoing rumours of interest from Arsenal - but Owen feels the Algeria international is unsuitable for Liverpool's system.
Internationally, he has been capped thirty-four times for his country, scoring eight times and he appeared at the 2014 World Cup finals.
But despite having previously handed in a transfer request and revealed a desire to play in the Champions League, Mahrez is not keen on a move to Liverpool.
"The amount of goals he has scored from outside the box is just ridiculous".
Speaking at his post-match press conference following the draw at Stamford Bridge, Puel said: 'We can see from today he is enjoying his football, he is happy in playing, in training, he is happy with us and his team-mates.
"I think that if he does leave Leicester it will happen close to when the transfer window closes".
Mahrez is rated at around £50m.
Manager Jurgen Klopp is wasting no time in bringing in a replacement for the 25-year-old and has his eyes set on Mahrez who won the 2015-16 Premier League title with Leicester.
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