Akpan left the Broadfield Stadium to join Reading for £600,000 in January but has found first-team opportunities limited this season.
However, Barker feels the chances of bringing the 22-year-old back to Sussex are "very slim".
He told the Argus: "I saw that rumour too but I don't know how it came about. Obviously Steve (Coppell, director of football) has good contacts at Reading so the possibility may have cropped up but it hasn't gone any further than that.
"If we had the chance to sign Hope it is something I would seriously consider but I would say the chances are very slim. I don't know what plans Reading have for Hope but from a financial point of view it would be tough for us to do anything.
"I would also query whether Hope would want to drop back into League One after working so hard to get to a higher level."