The 28-year-old, who faced an uncertain future in Manchester having been sold by manager Jose Mourinho during the pair's time at Stamford Bridge, is out of contract at the end of 2017-18 and he wants to extend his time at United.
"I have two years left on my contract and I would like to stay beyond that," Mata said in quotes published by the Mirror and The Sun.
"I am happy here and obviously since I came we have won the FA Cup, Community Shield and now we have another chance to win a trophy.
"I am thinking that the fans are amazing here even in the bad moments so I am thinking what happens if we win the Premier League or Champions League in the future years it will be incredible to celebrate them so I have that in my head."
Mata can add an EFL Cup trophy to his collection if United beat Southampton in Sunday's final at Wembley.