The France striker, 18, is one of the hottest properties in European football having scored 13 goals for table-toppers Monaco in Ligue 1 this term and a further five in their run to the Champions League semi-finals.
Earlier this week, Arsenal boss Arsene Wenger admitted the club do not have the financial muscle to compete for Mbappe's signature if he were to become available.
But Pires, a member of the Gunners' famed 'Invincibles' side of 2003-04, believes he will head to Emirates Stadium and that Wenger is the ideal man to nurture his blossoming talent.
Speaking to Bwin , he said: "I do think Arsenal will sign him.
"The problem is how much. Mbappe has the potential to play for Arsenal and Wenger is the right manager to manage him.
"Monaco and Arsenal are very similar in clubs, so it won't be much of a transition."
The comparisons between Mbappe and Henry are obvious, with both having started at Monaco while possessing pace and a deadly finish in front of goal.
But Pires believes it is unfair to already be mentioning Mbappe in the same league as the Gunners' record goalscorer.
"The comparison is unnecessary, he's not ready to be compared to Thierry. Mbappe is a very similar player but to compare the two players would be unfair," he added.
"I hope that Kylian can follow in the footsteps of Thierry Henry, he has the same profile as Thierry - quick, strong and a great finisher but he's very young so I would hold off on comparisons just yet."