Hibs enter the weekend's fixtures in fourth place in the SPL, slipping following successive losses to Inverness and Motherwell.
With the Rugby Park match followed by a Boxing Day clash with Ross County, a home fixture with Celtic and the Edinburgh derby at Hearts, Fenlon knows the festive period is crucial for his side.
He has sought to temper expectations for a side which narrowly escaped relegation last term, but is eager to take an optimistic approach rather than consider what might happen if his side struggle ahead of January's winter break.
He said: "There's the potential that if it goes well for us we could be second. That's the way we're looking at things.
"Four games in a short space of time, we want to make sure we pick up three points in the home games and then get something on the road.
"If anybody can go and pick up four wins it would put them in a great position. We've said from the start that we want to be a top-six team at the end of the season. That's still the goal.
"We've had a decent start. We've had a couple of bad results over the last two weeks, so we need to make sure we get back to winning ways."