All three interviews will be conducted at Shea Stadium on Wednesday by Mets executives, who hope to name a new manager by the end of the week.
Randolph, who spent this past season as Joe Torre's chief lieutenant as the Yankees' bench coach, is considered the front-runner.
Jaramillo, currently the hitting coach with the Texas Rangers, is expected to be offered the same position with the Mets, although Jaramillo has made it known that he is interested in managing.
Collins is a dark horse in the equation – the former Astros and Angels manager was not strongly considered going into his interview, but impressed enough to earn a second go-round.
GM Omar Minaya's other official interviews, Carlos Tosca and Jim Riggleman, were not invited back.
As expected, the Mets exercised a $2 million buyout on the contract of outfielder Richard Hidalgo, turning down a $15 million club option for the 2005 season. The move made Hidalgo a free agent, and it is believed the outfielder would be amenable to re-signing with the club.