Lampard's long-awaited move to incoming MLS franchise New York City was confirmed on Thursday after the England international midfielder signed a two-year deal.
With New York City not in action until the 2015 season, there has been talk of Lampard - Chelsea's all-time leading goalscorer - following high-profile recruit David Villa to fellow City Football Group-owned side Melbourne City in a temporary deal to keep fit.
Australian newspaper the Herald Sun published a report this week dismissing suggestions the 36-year-old would be joining Villa at the Melbourne club, who are also bankrolled by Premier League champions Manchester City.
However, Reyna told Sky Sports News a loan spell Down Under could be on the cards.
"There's that possibility, but we really haven't spoken about it," Reyna said.
"We wanted to make sure that Frank had his vacation that he's earned and is well deserved after so many years in the Premier League as well as the World Cup.
"We're going to sit down this week - he's here in New York for another week or so - and we'll have those discussions on just planning what we do with him for five months and that is an option.
"But we just need to speak together as a group, with Manchester City as well, and see what they think as far as our group.
"But one thing for sure is we're really confident he looks after himself and that he'll be ready to go in January 2015."
