The forward's struggles during the 2021-22 campaign led to suggestions that he was considering his future at Old Trafford, with a number of sides said to be keeping an eye on his situation.
However, Rashford will be staying with the Red Devils this summer, and he was in the starting side against Liverpool in the team's pre-season opener on Tuesday, playing 45 minutes of their 4-0 win.
The 24-year-old believes that he can achieve "a lot" under Ten Hag's leadership, and he is looking forward to having "a fresh start" under the Dutchman.
"I think we can do a lot together. For me, it's a fresh start and something I'm looking forward to. I think the first two and a half weeks of training have been good, we're a lot fitter than we were last season and also, we're making mistakes along the way, so we have a lot of room for improvement," Rashford told reporters.
"I'm in a good place right now and I'm looking forward to getting more games under my belt and getting ready for the season."
Rashford also believes that his long break over the summer will also help him in terms of the new season, with the attacker not involved in England's UEFA Nations League squad in June.
"I think it's been a bit unnatural for me to have such a long break in the summer, I had just under four weeks. So, I had a long break physically and mentally as well," he added.
"So, it's an opportunity to refresh and get ready to go again. It's always the case every season, whether you win or lose, so I just used that opportunity to do what I've always done and just refocus.
"I think this is the first year I've been with the team from the beginning and to be honest, I already feel a lot better than usual when you go away for the internationals and come back midway through the pre-season. So, like I said, it's important for me to get a fresh start and I've been given that opportunity. I feel fresh and I feel ready."
Rashford has also suggested that the team's struggles during the 2021-22 campaign made it more difficult for him to bounce back from his difficult moments.
"For me, I always say it's a lot easier to make mistakes in a team that's winning. We won the last game against Liverpool, but we made a lot of mistakes, so it gives us a huge space for improvement. Individually it's the same thing," said the Englishman.
"If you make mistakes in a winning team, it's a lot easier to come back and improve. When you're losing, it's difficult because we're all sportsmen and we don't like to lose so we have to just refocus and try our best to win the next game."
Rashford struggled to make his mark for the Red Devils during a difficult 2021-22 season, managing only five goals and two assists in 31 appearances.
The forward, who has scored 93 goals and registered 57 assists in 302 appearances for Man United in all competitions, is in line to make his second appearance of pre-season against Melbourne Victory on Friday.