Relegation-threatened Sunderland (6-7-16) are now second from bottom and four points from safety.
The Black Cats suffered their fourth defeat in five matches Wednesday when they lost 2-1 at Liverpool. Steven Gerrard and Daniel Sturridge gave the Reds a two-goal lead before Sunderland substitute Ki Sung-Yueng scored with a header on 75 minutes. The Black Cats were the better team in the final 15 minutes and were unlucky not to grab an equaliser as the Merseysiders held out to claim all three points.
Poyet was disappointed with the result at Anfield but pleased with the way his side battled against the title-chasing Reds.
"Liverpool were calling for time and trying to finish the game," Poyet told the Sunderland website. "You could tell how happy their fans were to hear the final whistle. I'm not happy that we lost, but I'm proud of how we approached the game.
"A result against West Ham now would be perfect for me because we have shown the type of attitude to go out and score goals and try and win the game and I want to see this again."
West Ham (9-7-15) moved up to 11th place and are now eight points clear of the drop zone after ending a run of three straight league defeats with a 2-1 home win against 10-man Hull City on Wednesday. The Hammers made hard work of beating a spirited Tigers side and were jeered by their own supporters at halftime and full time.
Hull goalkeeper Allan McGregor was sent off after 26 minutes for bringing down Mohamed Diame in the penalty area. Mark Noble beat substitute 'keeper Steve Harper with the resulting spot kick to give West Ham the lead. McGregor, who suffered a kidney injury in the challenge with Diame, later had his red card rescinded by the English Football Association.
Tigers striker Nikica Jelavic equalised just after the interval before a disastrous own by defender James Chester on 54 minutes gifted all three points to the Hammers.
West Ham manager Sam Allardyce was delighted with the result and defended the way the Hammers played to secure a much-needed victory.
"This is certainly a big relief after we lost three games on the trot for the first time in the Premier League," Allardyce told the West Ham website. "It wasn't about anything else other than winning the game and if we could have won with a lot more flair and ability, that would have been fine, but sometimes you have to win ugly.
"We've got a bit to go still and we've got to focus and concentrate, but that was a massive three points for us. We don't want to do anything other than get results wherever we go, starting with Sunderland on Monday night."
Sunderland will have Fabio Borini available after the on-loan Italian forward was ineligible to play against parent club Liverpool in midweek. However, fellow striker Steven Fletcher is sidelined with an ankle injury.
West Ham have injury concerns over defender James Collins (calf) and midfielder Matt Jarvis (thigh), while defender Joey O'Brien (shoulder) and striker Marco Borriello (calf) are definitely out.
The sides played out a goalless draw at Upton Park on Dec. 14. The Hammers have won just one of their last six matches at the Stadium of Light, a 1-0 victory in November 2008.