The A's plan to send Ramirez, who remains at extended spring training in Phoenix, on a 10-game Minor League assignment before they call him up.
Ramirez, who signed a Minor League contract with the A's, is currently suspended for violating baseball's drug policy for a second time.
"He knows where he is in his career," Melvin said. "And he knows the effect he can have on young guys."
As for Ramirez's role when he returns, Melvin said Sunday, "We've got to get there first."
"DH has been his role and that's what we envision him doing," Melvin continued. "We'll have to see what we'll do, roster-wise."
Ramirez, a career .312 hitter with 555 home runs and 1,813 RBIs to his credit, batted .059 in five games with Tampa Bay last season.
This will be Ramirez's 20th Major League season. Ramirez will turn 40 on May 30, when the A's are scheduled to play in Minnesota.