Fenlon hopes to end on a high
Reported Swansea target Iago Aspas will not be available during the January window, his agent has warned.
The 25-year-old striker has attracted interest from several of Europe's top clubs with his performances for current club Celta Vigo - and Michael Laudrup is rumoured to be lining up a move.
But his agent, Felix Gende, said: "It's clear that there are a lot of clubs following Iago because of the season he is having, but right now it is impossible that he leaves for another club in January.
"He is focused on helping his team retain their Primera Division status. Come June, when there are a lot more transfers, God will say what happens with his future."
Aspas' 23 goals last season inspired Celta to promotion to the Primera Liga, and he has netted six times this season in Spain's top flight.
The 37-year-old is taking his time to make a final decision on what is set to be the last move of his career, having been linked with clubs in England, France, China and Australia.
A spokesman for Beckham said: "There are a number of serious proposals on the table from a host of clubs across the world.
"David is no hurry to make a decision, the key is making the right one as he has always done successfully in his career.
"It's early days in the process. David is enjoying spending quality time with his family over the holidays."
The former England captain ended his five-year stint with Los Angeles Galaxy on December 1 after winning a second MLS Cup.
Hibs are fourth in the SPL, but have four points from their last seven matches after the 1-0 loss to 11th-placed Ross County on Boxing Day.
Leaders Celtic are an entirely different proposition to the men from Dingwall, but Fenlon is optimistic after drawing 2-2 at Celtic Park earlier this season.
Fenlon, whose side play Hearts in the Edinburgh derby on January 3 before the mid-season hiatus, said: "It's a big week for us. Celtic at home and Hearts away are massive games, but they're great games to look forward to.
"We shouldn't have to worry about getting people up for the next two.
"We feel we're capable of getting something out of both games.
"It's important we approach them in the right manner."
Fenlon bemoaned the tempo set by Hibs against County, who were content to put men behind the ball in a dull encounter. Celtic's approach will be different.
"You probably won't have as much as the ball as we did yesterday, but you've got to have a game plan and make sure you carry it out properly," Fenlon said.
"Retention of the ball against a team like Celtic is really important, your concentration levels have to be really high as well because they've got players in all positions that can cause you problems.
"We've got good players, we've got a good crew there and they work tremendously hard. To be overcritical of them is not really fair.
"There's not many times where we've played here and not got to the tempo we want.
"We just need to make sure we approach every game in the same manner. We've got to make sure when we play the likes of Ross County at home it's as big a game as Celtic."
The winter transfer window opens in less than a week, but Fenlon is still awaiting news on loanees Leigh Griffiths (Wolves), Ryan McGivern (Manchester City) and Jorge Claros (Motagua, Honduras).
Fenlon would like to retain all three, but has targets lined up should any of them leave at the end of their current deals.
"We'll wait and see over the next few weeks," Fenlon said.
"We've got a list together. If they don't stay we need to have replacements.
"It's a difficult scenario at the moment. We can't make the final decision on that."