Vieira took charge of Strasbourg last season after Chelsea's umbrella company BlueCo had bought the club.
He guided the team to a 13th place finish.
“Strasbourg 10 years ago was in the lower levels, so they’ve made their way up in the last 10 years, so there is a big change because now one of the owners is Todd Boehly, so we are part of the Chelsea family,” he told the Stick to Football podcast.
“The ambition is to play European football in the next three years. Of course, coming from this year, there is a big turn of young players, and this year was challenging and difficult – we struggled and went through some difficult periods.
“Hopefully, we will keep our best young players, we’re going to try and improve the team and try to finish in the top 10 next year. Then, why not play European football in two years’ time from now?”