After finishing third in their Champions League group stage, Manchester United dropped down to the Europa League and they will face Real Sociedad in the first leg of their Europa League last 32 tie on Thursday night.
The Premier League giants are favourites to beat the Spaniards and make it to the last 16 of the competition but many believe Sociedad are not going to be pushovers for the Red Devils.
Real Sociedad are also in the Spanish Cup final and there are suggestions that the club should prioritise winning the domestic cup competition over progress in Europe.
But Illarramendi stressed that they will focus on both and insisted that while Manchester United are going to be tough opponents, his team are good enough to beat them.
He told Mundo Deportivo: “No, we want to win the cup and do nice things in Europe.
“We now have a great rival in front of us, tough, but we are capable of eliminating Manchester and moving forward in Europe.”
Manchester United beat Sociedad in the Champions League last 16 tie in 2013 but Illarramendi was at Real Madrid then.
The Sociedad captain is hopeful that the result will be better this time around.
“I want to enjoy it.
“I lived that tie like one more fan. Let’s see if things are better for us now.”