Maritzburg required extra time to beat the ABC Motsepe League side 3-1 in the last-32 of the Nedbank Cup in Soweto on Saturday.
Davids gave credit to their opponents after the match at Dobsonville Stadium.
"I think the Swallows supporters, the coaching staff, management and the directors can be proud of the team's display," said Davids.
"They put up a brave fight. They should be in the PSL. South African football needs Swallows with their rich history and the support behind them."
Swallows, one of South Africa's oldest clubs, bought the third tier status of Orange Vaal Professionals last year, and are rumoured to have recently purchased the National First Division franchise of Cape Town All Stars.
Dube Birds coach Isaac Mphasane denied any knowledge of the club changing hands.
"I want to focus on the Motsepe League. I don't know anything regarding the [sale talk]. We are left with 10 games and my focus is to make sure we perform well in those remaining games," he said.
The former Soweto giants went into free fall after being relegated from the Absa Premiership in 2014/15.