The Scotland international was released by Middlesbrough following an injury-plagued two-and-a-half year spell with the npower Championship side. That sparked rumours that he could be headed for a return to Edinburgh with his old club.
But Fenlon insists cash restraints simply won't afford him that luxury, although he did joke a act of generosity similar to that shown by former England skipper David Beckham - who signed for Paris St Germain after vowing to hand his salary to a French children's charity - may alter things.
He told Press Association Sport: "Kevin's name hasn't cropped up here. With someone like that, and it's similar with some of the other ex-players, as soon as they become available they are linked with Hibs.
"But we are not in a position financially to do anything else. We have done as much as we can - unless he wants to do a Beckham. He's a fantastic player and I'm sure he won't be short on offers."
One player who did check in at Easter Road was Barnsley winger Matt Done. Done was snapped up on a loan deal until the end of the season, with his move confirmed just minutes before Thursday's transfer deadline.
Fenlon will put the player straight into his squad for Sunday's William Hill Scottish Cup fifth-round meeting with Aberdeen and is optimistic that the 24-year-old will make a positive contribution.
He said: "We had identified some players we wanted to look at over the past few weeks and had two or three on the radar for a wee while.
"It was a position we knew we had to fill to give us a different option. I've spoken to people who have been involved with Matt and got some really good reports on his ability and him as a lad, so we were pleased to get him in.
"He can bring a bit of energy to the team, he can also go and play up top which gives us another option. Maybe he can gives us that little spark that we are missing."