Alonso has struggled since moving back to McLaren in 2015, after the British manufacturer switched from Mercedes to Honda power units.
His best finish has been fifth on two occasions - Hungary in 2015 and Monaco in 2016 - with 10 retirements in 26 starts over a season and a half.
However, Boullier believes McLaren have made a big improvement with their Honda partnership, and insists 34-year-old Alonso can become world champion once again, after he triumphed with Renault in 2005 and 2006.
"I think Alonso is not prepared to retire at all," Boullier told AS.
"I am certain that if he trusts the project McLaren Honda are doing, he will finish becoming champion."
He added: "I really believe in the project, I see progress, we are going forward.
"McLaren are prepared and we have better packages now with the chassis and motor."
Alonso's contract runs out at the end of the 2017 season.