The goalkeeper was hurt in the second half of United's 1-0 win at St. Mary's in what remains the Magpies' last Premier League game as a result of the coronavirus outbreak.
He had been ruled out for at least the rest of this month, but with the Premier League now postponed until at least 30th April, the 31-year-old Slovakia international is now likely to be fit by the time the top flight programme resumes.
Dúbravka, who has been working with club physio Michael Harding from a safe distance, spoke to nufc.co.uk to update supporters on his progress.
He said: "Every morning I'm visiting the clinic with Mike and spending the time with him to heal my knee.
"I've also got my programme in the gym, so I'm trying to be fit and ready as soon as possible. I think I'm doing similar things to my team-mates."
With United's Benton training ground currently closed, Dúbravka has been working out at home - and occasionally outdoors with the help of the French Bull Jack he shares with his partner, Lucia.
He added: "I'm trying to spend time with my girlfriend, as she is the only (family member) in England for me, and it will be tough for her as well, so we are trying to spend time with our dog for long walks in the woods where there are no people.
"There's not much to do in this time where you have to be careful - you have to stay at home most of the time, you have to stay away from people, but we are obviously very active people so we are trying to do as many things as we can, especially around the house."