With the Citizen looking to extend their record of scoring the most goals in a single season, anything is certainly possible.
Spurs host Leicester City who have had a disappointing end to their season; the Hammers host Everton in what could be Wayne Rooney's final club game in England.
"At the end we are not in a good position, but we have a tiny chance to stay in the Premier League and we will do our best".More news: Homeland Security Secretary Kirstjen Nielsen doesn't directly deny resignation report
Former Wales striker Iwan Roberts said the decision on Carvalhal's future was "crucial" to Swansea's future as they plan for life in the Championship after seven successive campaigns in the Premier League.
They've two games left to make them mathematically safe, but they don't come easy against Chelsea away on Wednesday and Arsenal at home on Sunday.
Huddersfield Town's draw against Chelsea on Wednesday night virtually relegated the Welsh club, who trail 17th-place Southampton by three points and with a goal difference worse by nine goals going into the final day of the season on Sunday.More news: Give Donald Trump Nobel Peace Prize
They're three points clear of Swansea and Southampton now and they will be certainly nervous going into their game at Stamford Bridge.
With Swansea City's fate to be sealed this weekend, there looks set to be big changes at the club regardless of the outcome.
An example scenario that would see Swansea avoid relegation is them beating Stoke 4-0 and Manchester City battering Southampton 6-0.More news: Merkel reaffirms Germany's commitment to Iran nuclear deal despite United States withdrawal
Only victory against Stoke, coupled with Southampton losing to Manchester City and a 10-goal turnaround would save them. But their form has collapsed since then. Home advantage will be key, but survival is in their own hands.