The 31-year-old Irishman played the second half of Hibs' 2-0 friendly win over East Fife on Saturday as he looks for a club after leaving St Johnstone.
But with the financial uncertainty engulfing the Scottish game amid the fallout from the collapse of Rangers, no deal is imminent.
Fenlon told Hibernian TV: "We have had Alan in training for a week.
"He's a great professional and a very, very good player. He's probably someone we could do with around the place.
"Whether we are able to do it at the moment, I'm not too sure with the way things are. So we'll just have to wait and see."