"We don't adopt their views, we don't adopt their policies", he said.
The interview is Mr Barnier's first since being appointed the European Union's point man on Brexit.
Prior to the election, Mrs May had said that the United Kingdom would be leaving the single market and the customs union and she repeatedly insisted that "no deal is better than a bad deal".
Brexit Secretary David Davis will play a key role in negotiations with the European Union, alongside Liam Fox, International Trade Secretary and Boris Johnson, Foreign Secretary.
After a tumultuous week that pitched Britain into its deepest political crisis since the Brexit referendum a year ago, May's future was uncertain, darkened by her botched gamble on a snap election and muted response to a deadly fire in London.
Her spokesman said Britain would not change its stance on Brexit, though May told her lawmakers she would seek a broader consensus in the party on her approach.
Video: What does the election result mean for Brexit?
Barnier has said he wants to wrap up a Brexit deal by October 2018 so it has time to get through national parliaments and the European Parliament in time for Britain's departure from the bloc at the end of March 2019. "We will negotiate in good faith but it is a negotiation, we recognize there will be an exchange of views and we will take that forward in a spirit of genuine cooperation". "We are ready as soon as the United Kingdom itself is ready", he said.
Talks to prop up May's government continue with DUP
Theresa May will meet with Sinn Fein , the UUP, the SDLP and Alliance Party in separate meetings at Downing Street on Thursday afternoon.
Brexit talks will begin Monday.
As May attempts to cobble together a majority, the EU's Barnier said he will hold talks with British envoy Olly Robbins on Tuesday to organise the negotiations.
It is not known how fruitful the talks were, but sources close to Mr Barnier have told Sky News that the two sides have agreed to have further contact at later this week.
It would also leave open the option of walking away from the negotiations with no deal in place - a decision that many businesses warn could be disastrous.
According to what an EU official familiar with the negotiations arrangements told New Europe, the EU side is looking at 4-week negotiation cycles, while the initial talks are expected to focus on early issues about the negotiating regime, or as the EU official referred to, it is going to be "talks about talks".
In Strasbourg where members of the European Parliament are holding the monthly plenary, MEPs seem broadly frustrated and impatient by Britain's domestic politics and the delay they are causing. "I think it's unlikely there will be any announcement today", a DUP spokesman told AFP.
"The name of the game is a withdrawal treaty with a deal because ultimately no deal is bad for us and it is catastrophic for the UK".
"This new arrangement is very unsettling and people are concerned and anxious about what it may mean", Sinn Fein MP Michelle Glidernew told AFP.