The Ukrainians made an offer last month but Fulham promptly turned turned it down, insisting Kacaniklic was a first team player whom had no intentions of leaving.
Kiev, though, think both club and player can be persuaded and are lining up an improved bid for the 21 year-old, who signed a new long-term deal in the summer.
It is unlikely that Martin Jol will budge on his original stance, however. Despite brining in Urby Emanuelson, who can play on the left wing, the Dutchman believes Kacaniklic is a vital part of the team and has a particularly bright future ahead of him.
The signs are certainly promising. Having made 19 appearances already this season, the Swede has hardly put a foot wrong and has established himself as one of the best wingers at the club.
With Emanuelson set to feature in the middle, as he did on his debut against Manchester United, Kacaniklic has little to worry about in terms of retaining his first team spot.
Technically gifted and with a stunning turn of pace, the 21 year-old's only wish would be a greater end product. He has chipped in with goals - though not many - but his crossing could well be improved.
It's something that is easily learned over time, however, so we can only hope Fulham stand firm on the second time of asking.