Jones, who in late May agreed to a contract worth $900,000, has completed his 50-game suspension that occurred when he violated baseball's Minor League drug policy.
In December, Jones agreed to a $1.3 million contract with the San Francisco Giants. One month later, Jones' contract was voided after he failed a team-administered drug test that was part of his physical.
San Diego director of player development Randy Smith, who is flying to the Dominican Republic next week, said Jones physically looks like a young Adrian Beltre.
"We're anxious to get him going, [he's a] good-looking prospect and in our opinion one of the top hitters available on the international market," Smith said. "He's been working out daily at the [Padres' Dominican Republic facility] and watching our games.
"We have had him in some simulated games to try and keep him game ready."
In May, Smith said Jones is "6-foot-3, 195 pounds and has a great build, broad shoulders. He has good bat speed with plus-power potential, a plus arm and good agility for his size. I like the makeup, too. He's one of the premium offensive guys over there.
"He's pretty advanced as far as his approach."