Sagna, who joined the Gunners from Auxerre in 2007, is currently recovering from a broken leg suffered in Arsenal's draw with Norwich earlier this month. The Frenchman is aiming to return to action at the start of next season, but is "devastated" to be missing out on Euro 2012 this summer.
Van Persie, meanwhile, is off contract next summer, and while the likes of Barcelona and Manchester City have been linked to the Dutchman, Sagna says the club captain will lead the side out again next term.
"I'm confident Robin will stay," Sagna is quoted as saying in the Daily Mirror. "He was a complete professional from the beginning until the end and helped us into third. We want to keep him.
"Everyone is so grateful to him for what he's done for the club and how important he is. He is our captain and he takes his role and responsibilities very seriously. He gives everything as a player and captain."
Arsenal have been linked with a move for M'Vila for some time, with manager Arsene Wenger understood to be an admirer of the France international. Sagna feels his compatriot M'Vila could be the perfect fit for the Gunners as they aim to break their seven-year trophy drought.
"We want more players to come to the team," Sagna said. "Lukas Podolski has arrived already and he is a German international and a quality player.
"M'Vila can make a great impact. I'm not sure about his English but it took me time to learn. But I think he would suit us as well. Arsenal is a French-speaking team and it will help him settle. I think we can be contenders this coming season. We showed a lot of people what we could do last season.
"Last summer, people were talking about Cesc Fabregas and Samir Nasri leaving. It was a difficult season in the Premier League and, for all football fans, it has been a crazy, crazy season. It was difficult for us but we kept fighting. I think it shows we can be strong contenders next season.
"This season has given us great belief for the season coming. Arsene Wenger has always given us the belief and confidence and made the decisions to help us through. If we had not had so many injuries then I think we would have gone closer to winning trophies this season."