Sainz joined Ferrari from McLaren in 2021 and last April - under then principal Mattia Binotto - signed a contract extension to the end of 2024.
Monegasque Leclerc, overall runner-up to Red Bull's double world champion Max Verstappen last season, is also contracted to the end of 2024.
Leclerc drove for Vasseur's ART team in the GP3 junior series and made his F1 debut with Ferrari-powered Sauber in 2018 when the Frenchman was in charge.
However, Vasseur, who was Renault team boss before moving to Sauber, told reporters on a Zoom call that he also had past connections to Sainz and rated him highly.
"I started a discussion with Carlos and Carlos's management when I was at Renault, to attract him and to sign the contract," he said.
"Then he joined a bit later. When I was at Sauber I tried to sign Carlos again without success and I said OK, if I want to (work with) Carlos the best way is to join the team where he is," joked the Frenchman.
"We always had a very good relationship. I trust him and I think he showed in the last couple of years that he's a potential winner that's very important for the team.
"We won't have a number one and number two. The organisation is crystal clear that they have to do their job and if at one stage I will have to take action for Carlos or for Charles I will do it."
Leclerc won three races last year, and took nine pole positions, while Sainz claimed his first win in Formula One at the British Grand Prix and finished the season fifth overall.
