The former Stevenage and AFC Wimbledon man has been an unused substitute for the last three matches.
"We have been playing a different way of late, without a big man up front and using two smaller strikers," Buckle said.
"With that in mind we have decided to make Byron available for loan or permanent move."
Harrison joined Cheltenham from the Dons for a fee of £25,000 in January 2013. He was the club's leading scorer last season with 15 goals, taking the supporters' player of the year award.
The 27-year-old has netted seven times this term, including a hat-trick against Swindon Town in the 5-0 FA Cup first round victory at Whaddon Road.
He scored the first goal of Buckle's reign as manager, in the 1-1 home draw with Oxford United on November 29, but after three starts under the new boss he lost his place.
Harrison joins left-back Paul Black on the list of players available as Buckle continues to reshape his squad.
Jason Taylor, Adam Powell and Raffaele De Vita have all left the club, with Jack Dunn, Kevin Stewart and Lloyd Jones arriving on loan from Liverpool this month.