The sale price, first reported by the Wall Street Journal, would eclipse the record of $2.4 billion (£1.7bn) for an MLB franchise, set when Steve Cohen bought the New York Mets in 2020.
The Wall Street Journal said that Feliciano will be designated the controlling owner.
The 53-year-old from Puerto Rico is the co-founder and managing partner of California-based private equity firm Clearlake Capital.
In 2022, Clearlake was part of the Todd Boehly-led consortium that purchased Chelsea for 4.25 billion pounds ($5.3 billion). Jones is the chief executive officer of Supercharged, a media and personal development company.
The Wall Street Journal, citing "people familiar with the matter," said the sale is expected to be announced early next week. It would be subject to the approval of 75% of MLB's team owners.
Multiple US media outlets reported that Feliciano and Jones beat out bids from Tom Gores, owner of the NBA's Detroit Pistons, and the NBA's Golden State Warriors owner Joe Lacob, as well as Dan Friedkin, owner of the Premier League club Everton.
The Padres have been owned by the Seidler family since 2012, but were put up for sale in November by relatives of late owner Peter Seidler.
The Padres are the only major professional sports team in San Diego. Free spending on stars such as Manny Machado and Fernando Tatis Jr. has helped them make the playoffs in three of the past four seasons, but they have yet to win a World Series title.
A sale would come as MLB girds for labor talks that most expect to be contentious, with owners expected to pursue a salary cap that players bitterly oppose.