The 40-year-old South African will be the youngest captain of the Internationals in the event's history.
British Open was called off until 2021 as a result of the coronavirus pandemic.
The 149th Open was scheduled to take place at Royal St George's Golf Club in Kent in July.
Top golfers find it easier to get through the lockdown than most people, with many having personal gyms, practice facilities and swimming pools at their homes.
The coronavirus pandemic has prompted three of the five women's majors to be rescheduled with tour action suspended until late May at the earliest.
Golf Week reported that USGA officials are holding off on an announcement about the major championship.
Mid-July offers the Great Lakes Bay Invitational, a pairs event July 15-18 at Midland, Michigan, and no other events before four European stops in August.
Asked in a Twitter chat Sunday night about the chances for a rematch with Woods, Mickelson tweeted, "Working on it."
Mickelson defeated Woods in 2018 in a one-on-one matchup for $9 million in a pay-per-view event staged in Las Vegas.
Paul Casey, a member of the winning Europe team in France in 2018, has called for the tournament to be put back 12 months.
The only prior years the Masters has not been contested in April at Augusta National since its 1934 debut were 1943-1945 due to World War II.
The Cactus Tour will stage its 12th 54-hole event of the year, and third since major US sports league went silent, starting Tuesday at Sun City Country Club in Arizona.
Europe's clash with the United States is scheduled to be played at Whistling Straits in September.
The Ryder Cup is slated for September 25-28 in Whistling Straits, Wisconsin.
A statement from the PGA Tour said Lange had no symptoms and was expected to make a full recovery after a period in quarantine at his home in Johannesburg.