In a post retweeted by Tiley, the Australian Open said Sandgren had been cleared to fly by the relative health authorities.
Keys also added that she wasn't hoping to wait to find out if she could travel late to Australia and get a chance to play the first Major of the year.
A quarter-finalist at Melbourne Park in 2018 and 2020, Sandgren was supported by Tennis Australia, who said they followed Victorian government guidelines in allowing him onto the flight.
However, that could prove hard with players and officials required to arrive in Australia during a 36-hour window from Thursday and needing to serve a mandatory isolation of 14 days.
The men's qualifying tournament for the Grand Slam took place in Qatar.
Sandgren later tweeted to clarify: "My two tests were less than (eight) weeks (apart)".
"Tennys Sandgren's positive result was reviewed by health experts and determined to be viral shedding from a previous infection, so was given the all clear to fly", Ms Neville tweeted.
The five-time Australian Open runner-up pulled out of last week's ATP event in Delray Beach, Florida, as he wanted to "minimise the risks" in the run-up to the year's first Grand Slam. "I was sick in November, totally healthy now", his tweet read.
Any players or official that tests positive will be moved to a dedicated hotel away from the rest of the travelling contingent. "There's not a single documented case where I would be contagious at this point".
Organisers Tennis Australia were not immediately available to comment.
The Australian Open has already been delayed three weeks because restrictions in place for the COVID-19 pandemic, and is set to open on February 8.
Those playing in this year's Australian Open must complete a two-week quarantine upon landing in the country.
Players are due to touch down in Melbourne on charter flights from seven cities, although the game's biggest stars, including Novak Djokovic, Rafael Nadal and Serena Williams, will arrive in Adelaide and quarantine there.
Once a negative result has been returned, players can train within a strictly supervised environment for five-hours per day, and players and their teams will be tested every day during quarantine.
John Isner will not play the 2021 Australian Open.
Djokovic, Rafael Nadal and Serena Williams will be among a group of players involved in an exhibition event in Adelaide, South Australia state, on January 29.