The Brazilian forward is reported to be among those under consideration by Red Devils boss Jose Mourinho.
A reunion at Old Trafford has been mooted, but Willian has sought to distance himself from those rumours.
Instead, the 28-year-old has every intention of honouring a long-term deal at Stamford Bridge and helping the Blues to build on their Premier League title triumph by challenging for top prizes in Europe.
Willian told the Evening Standard when asked if he expects to be at Chelsea next season: "Yes. I have a contract with Chelsea until 2020 and I am very happy here.
"I have a great relationship with all the people that work at Chelsea and the fans too. They have been great to me since I joined.
"Chelsea are back in the Champions League next season and I am looking forward to playing in it again. It is a big, big target for us and we have to look to win that trophy next year."
While outlining his goals for the 2017-18 season, Willian is not finished with the current campaign just yet.
"We want to end the season with the double. We have the Premier League but we want the FA Cup too,” added Willian.
"This is a big game for us. It will be difficult against Arsenal and we have to be ready.
"We have to be focussed and play in the same way we have all season."
Willian has made 40 appearances for Chelsea in all competitions this season, netting a personal best 12 goals.