Rashford has been out since mid-January with a back injury, with United boss Ole Gunnar Solskjaer saying earlier this month the club would not rush his comeback.
The England international is making good progress, and suggests he will be ready to resume training once the squad are cleared to go back to work after the coronavirus pandemic.
"I feel much better," Rashford told Sky Sports News in the UK. "I have a scan in another couple of days and that should solidify it, but I feel much better compared to two or three weeks ago.
"I feel 10 times better now. For me, now it's just about getting ready to build back up to training and then playing games for the team.
"I'm in a much better place. I'm much happier than I was about a month ago, so things are looking positive."
Rashford says his recent rehabilitation has been carried out at home because of the restrictions put in place to control the impact of COVID-19.
"Everyone is just dealing with the circumstances as well as they can," he added.
"I've just been in my house doing my gym work and recovery, reading books, watching Netflix and just doing what I can do to make the time pass further.
"There's not really anything you can do that comes close to being in the changing room and being in the team, so I'm not trying to chase that high.
"I had to have time off anyway because of my injury, but I'm fortunate enough to have a bike in the gym downstairs. Not much in that sense has actually changed for me because I can still do my daily routine that I was doing."
Rashford is also heading up a campaign for the FareShare charity, which aims to raise £100,000 ($201,000) to help supply food to children who usually have free school meals but are currently unable to access them.
"I didn't know how high the numbers were of kids not eating at home other than school meals. That number kind of shocked me," Rashford said.
"And then I remember speaking to a friend who was saying there was an opportunity where we can help these people and FareShare allowed us to make it work.
"I don't think I've actually ever done something at such short notice before. I thought let's try and get to £100,000 ($201,000) and right now we're on £97,000 ($195,000)."