Arsenal have made a bid of £40m + £1 for the 26-year-old but Liverpool manager Brendan Rodgers says he wants the Uruguayan international to remain at Anfield.
And Mourinho, involved in a transfer saga of his own as he pursues Wayne Rooney of Manchester United, thinks Arsenal should go and get Suarez if they have the finances.
"I've no idea of the contractual situation of Luis Suarez," said Mourinho.
"But, I think if Arsenal has the economical potential to buy, and his manager decides Luis is the perfect buy for them, I think it's normal they make an offer.
"But I have no idea how it's going to end."
And Arsenal forward Olivier Giroud thinks their audacious bid for Suarez has sent a signal to the club's current playing staff.
"We need to show ambition and the offer for Suarez has done that," said Giroud.
"The club has to show the fans that we mean business. Me and my team-mates need it as well. It will be a really positive thing if we have a new striker."
Giroud is looking forward to the start of the new campaign and added: "The whole team is stronger now than it was a year ago. Last season's new players are all more established.
"And we've lost nobody this summer, which is the first time for Arsenal in maybe four years."