The Ospreys are angry they cannot finalise their last regular 2009-10 Magners League game against Newport Gwent Dragons, scheduled for 7-9 May.
Fellow Liberty Stadium side Swansea City could play a football Championship play-off game on Saturday, 8 May.
If the Swans do not make the play-offs, BBC Sport Wales wants to broadcast Ospreys v Dragons live on 7 May.
If Swansea make the play-offs, the broadcaster wants the Ospreys game to be on Sunday, 9 May.
Swansea City's entry to the play-offs depends on them beating Doncaster and Blackpool not winning their match with Bristol City. Both football matches are on Sunday 2 May.
An Ospreys statement read: "Ospreys Rugby would like to make known our disappointment regarding the scheduling of this this important [rugby] fixture, and the lack of flexibility and understanding from the Celtic League and our broadcast partners which has, we believe, seriously undermined the integrity of the Magners League, not to mention the inconvenience it has caused to our players, supporters and commercial partners.
"There are very real issues, both legal and logistical, that prevent us from being able to offer any form of guarantee that we can host a match on the Friday night, and these issues have been discussed at length with all parties from the outset.
"In fairness to the broadcasters, they flagged this issue with the Celtic League in the first week of February, suggesting a meeting to make suitable arrangements to avoid any fixture clash on final weekend of season.
"Sadly, this meeting never took place... this is quite clearly an unsatisfactory situation.
"It means that at best this will give us just six days to prepare for this game, and at worst, four days, causing great inconvenience to players supporters and commercial partners and we would like to apologise to everyone concerned."
The Ospreys are second in the league having already secured their Heineken Cup place for next season as well as ensuring a top-four finish for a place in the inaugural Magners play-offs.
They may need to beat the Dragons to ensure a play-off semi-final at home.
Meanwhile Munster, Cardiff Blues and Edinburgh are vying for the final play-off spot.
Magners League organisers Celtic Rugby have stated: "The League rules say that games must be played at the same time if they involve teams getting into the top four.
"But they don't specifically relate to teams getting into the top two. There's not a requirement for simultaneous scheduling to determine the order of the top four teams.
"Coming into Round 18 there are three teams who have already booked their places in the Magners League Play-Offs - Leinster, Ospreys and Glasgow Warriors.
"The fourth and final place is open to one of either Munster, Cardiff Blues and Edinburgh.
"Against that background, and needing to comply with our commercial obligations to the Welsh broadcasters, S4C and BBC Wales, to deliver at least two fixtures per weekend, it was decided to place the two fixtures that involve the three teams fighting it out for the final place at the same time on the same day - 1815 BST on Sunday, 9 May.
"The matches between Scarlets and Glasgow Warriors and Ospreys and Newport Gwent Dragons have a bearing on which teams will win the two home semi-finals in the play-offs.
"That is why they are both scheduled to be played at the same time on Friday, 7 May.
"In Wales, our broadcast partners S4C had first pick of the matches and chose to cover the game at Cardiff City Stadium.
"BBC Wales opted for the Welsh derby between the Ospreys and Dragons, asking for it to be played in their regular slot of 1905 BST on Friday night.
"However, because the Ospreys do not have primacy of contract at their home venue of the Liberty Stadium, there is a possibility that Swansea City might be playing there on Saturday, 8 May in the first-leg of the Championship play-off.
"If that happens, then the Ospreys' game will have to be re-scheduled for Sunday, 9 May."
Celtic Rugby say they have done all they can to meet their obligations, will look into the issues surrounding ground-sharing, and may demand teams nominate a second "home" venue to avoid such fixture complications in future.
Hands OFF
The Millennium Stadium would probably be the second option, I don't think Cardiff Blues will ever play at the Arms Park again, unless of course Thomas were to go and a proper businessman took it over, can't see it happening though unless Thomas drops off his perch.
Following Cardiff RFC all over from sunny Bournemouth in Blue and Black
Sardis Rd
noamber:Sardis Rd
Llandaff Fields might be a drier option even with the River Taff flowing through the middle
This time, it's become superfluous as the Swans didn't get into the playoffs.
However, it COULD happen in both the Liberty AND SdR!
Cardiff born and Cardiff bred Supporting rugby in Cardiff
..........."if it aint broke, then keep fixing it until it is!"
But it did impact on this year. It was the reason that the last round of fixtures were anounced late.