The Premier League season will be extended to a 39th game to accommodate a relegation play-off between Swansea City and Hull City, staged at a neutral venue, should they finish in joint-18th place, level on points, goal difference and goals scored.

Hull are 17th in the table, two points above Swansea, with three fixtures remaining for both clubs. Swansea’s goal difference is -29 compared with Hull’s -31, and the Welsh club have scored four more goals.

Should those records be identical come the end of the season, with a relegation place at stake, the Premier League would take the unprecedented step of organising a one-off match in line with the rules laid out in its annual handbook to decide which club retain their top-flight status.

Premier League rules state: “If at the end of the season either the league champions or the clubs to be relegated or the question of qualification for other competitions cannot be determined because two or more clubs are equal on points, goal difference and goals scored, the clubs concerned shall play off one or more deciding league matches on neutral grounds, the format, timing and venue of which shall be determined by the board.”

Paul Clement, the Swansea manager, admitted he was aware of the possibility of a play-off game but said that it is something he hopes to avoid. Asked whether he would take that scenario now, given Swansea are trailing Hull, he replied: “No. Although it’s two points, for me it’s much tighter than that because of what we’ve got [left to play], what they’ve got, all the different ramifications, especially when you involve Crystal Palace, and when you involve Tottenham and the Chelsea situation. I think it’s more even than the table shows, certainly from a mental point of view.”

Provision has been made for a play‑off game on two occasions in the past, albeit never before in relation to relegation, where the financial ramifications are so much greater. In 1996 tickets were printed for a play-off between Manchester United and Newcastle United to be held at Wembley in what would have been a title decider had they finished level. Manchester United ended up winning the league by four points.

Discussions were also held with Arsenal and Chelsea on the eve of the final round of fixtures of the 2012-13 season, when there was a possibility of the two clubs finishing the season tied for third place – automatic Champions League qualification was the prize – and unable to be separated on points, goal difference and goals scored. On that occasion Chelsea finished two points ahead of Arsenal.

It is understood the Premier League has not yet taken the step of consulting Swansea or Hull over the prospect of a play-off match, though the possibility of a 39th game has been considered by senior club staff for a little while.

Clement, meanwhile, has expressed his surprise that Mike Riley, the head of Professional Game Match Officials Limited, made no attempt to get in touch with him in the wake of Neil Swarbrick’s blunder at Manchester United on Sunday, when the referee awarded a penalty against Swansea that should never have been given after Marcus Rashford dived. “I chose not to put any call into the FA on this occasion,” Swansea’s manager said. “I felt that I had made my point very clearly in the media afterwards. But I have had no communication at all from anyone. The delegates’ report you get, but I’ve not heard anything from Mike Riley about that situation. It surprised me because of the nature of it and the position that we are in. I thought there might have been some communication.”

Swansea have been on the wrong end of several poor refereeing decisions in the last few months. Swarbrick denied Swansea what looked to be a clear penalty at Chelsea, Anthony Taylor erroneously awarded Burnley a spot-kick in March and Clement maintains that Mike Dean unfairly penalised Swansea prior to Manchester City scoring a late winner in February.

“We’ve had our fair share and they’ve all potentially cost us,” Clement said. “If we are given a penalty at Chelsea and score it is 2-1, though we did lose to a better team. But it could have been different against Man United and I am sure we would have got a point against Man City if that had been dealt with correctly. I can’t blame Neil Swarbrick for the decision [on Sunday], only for giving it if there was doubt, which I feel there was.”