Tusk's spokesman, Preben Aamann, told CNN's reporters that the EU will need to consult with the other 27 member states and produce an initial negotiation position.
The process would take anywhere between four and six weeks.
May has vowed to give MPs and peers a vote on the deal she negotiates. However, she also insisted that the UK will leave even if Parliament rejects the deal.
Before May announced the date she'll invoke Article 50, which is next Wednesday, European Commission President Jean-Claude Juncker was quoted in German newspaper Bild as saying that Brexit will not inspire other EU member states to leave the bloc.
"They will all see from the UK's example that leaving the EU is a bad idea," he said, citing unfavorable terms, including a £50bn "divorce bill" would need to pay to leave the bloc.
"On the contrary, the remaining member states will fall in love with each other again and renew their vows with the European Union," he added.
European Council President Tusk also said the EU would not be "intimidated" by threats from Britain that it would prefer to walk away from negotiations if it did not get its way.
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