The former Arsenal right-back says the Chilean attacker has the quality to have fit in with Henry, Bergkamp, Pires and co.
Lauren had already won the league and cup Double and a second FA Cup trophy by the time he was an integral member of Arsene Wenger's side which managed the ultimate achievement in 2003-04 by going unbeaten for an entire league campaign to win the title.
Alongside the Cameroonian in that side were such stars as club record goalscorer Thierry Henry, Dennis Bergkamp, and Robert Pires in perhaps one of the greatest sides ever assembled in modern English football.
The current Arsenal side, which finished second for the first time in 11 years this season, does not possess the same wealth of talent but still boasts such world stars as Sanchez and World Cup-winner Mesut Ozil.
Despite the undoubted class of Ozil, Lauren chose only to name Chilean attacker Sanchez when queried on which of the present players could stand up to his illustrious teammates.
When asked by Goal if any of the current Gunners crop could have played in the 'Invincibles' side, Lauren said: "Straight away I would say Alexis Sanchez. He’s the kind of player who gives 110 per cent in every single game.
"I think to achieve targets and success you need players like that. I like this type of player. You need charismatic figures within the Arsenal squad and he’s one of them."
Since arriving from Barcelona for around £35 million two years ago, Sanchez has scored 42 goals in 92 appearances for the Gunners in all competitions.
Though he has received criticism for his form in an injury-hit second campaign at the Emirates Stadium, his goals to games ratio stands up relatively well in comparison with last term, with a goal every 2.4 games on average this year as opposed to one every 2.1 matches in his debut year.