Hazard, 27, marked his 300th appearance for the Blues by scoring the winner as his side defeated United 1-0 in the FA Cup final at Wembley on Saturday.
Chelsea's failure to qualify for next season's Champions League has raised questions about Hazard's future, with reports linking him with Real Madrid refusing to go away.
When quizzed about his future after the FA Cup final, Hazard told BT Sport: “Now, we just need to focus, we have the World Cup, we have some holiday.
“We don’t talk about next season now, we talk about the World Cup and holiday.”
But, when pressed about what it would take for him to stay at Chelsea, Hazard - who also had man-of-the-match Rudiger encouraging him to remain in the same post-match interview - said: “I want Antonio Rudiger to play like this every game, and then I’ll stay, I promise I’ll stay. Because I want to play with him!”
"Eden Hazard please stay!"
"I need Rudiger to play like this every game, then I'll stay!"
The Chelsea pair's interview with @DesKellyBTS is hilarious pic.twitter.com/JmSFESzaG5 — Football on BT Sport (@btsportfootball) May 19, 2018
Hazard netted the all-important winner from the penalty spot after he was brought down inside the area by United defender Phil Jones.
The Belgium star's current contract at Stamford Bridge expires in 2020 with Chelsea keen to tie him down to fresh terms.
Speaking about Chelsea's cup final victory, Hazard added: “I think it’s a great feeling today, especially when we lost the final last year.
“We didn’t have a good season this year, but we finished well. I’m just happy for the fans today, it’s a great feeling.
“We wanted to finish the season with a trophy. We couldn’t finish in the top four, we don’t have the Champions League next season, but at least we have something to celebrate this year with the fans.”