But speaking at a press conference at the G7 summit in Biarritz, France, Mr Tusk said he would “not cooperate on no deal”.
Mr Tusk and Mr Johnson are due to meet on Sunday to discuss Brexit.
Since becoming prime minister, Mr Johnson has insisted the UK will leave the EU on 31 October.
Mr Tusk said Mr Johnson is the third British prime minister he will have met since the UK voted to leave the EU in June 2016.
He said: “The EU has always been open to co-operation. One thing I will not co-operate on is a no deal.
“We are willing to listen to ideas that are operational, realistic and acceptable to all EU member states.
“I still hope Prime Minister Johnson will not like to go down in history as Mr No Deal.”
The G7 summit – a get-together of most of the leaders of the world’s largest economies – comes with just over two months until the UK is scheduled to leave the EU at the end of October.
Mr Johnson wants to renegotiate the Irish backstop – a key Brexit sticking point which is part of the withdrawal agreement and aims to prevent a hard border on the island of Ireland after Brexit.
The EU has consistently ruled this out.
If implemented, the backstop – a last resort should the UK and the EU not agree a trade deal after Brexit – would see Northern Ireland staying aligned to some rules of the EU single market.
It would also see the UK stay in a single customs territory with the EU, and align with current and future EU rules on competition and state aid.
At a news conference on Wednesday with Mr Johnson, German Chancellor Angela Merkel suggested an alternative to the backstop might be achievable, adding that the onus was on the UK.
But the next day French president Emmanuel Macron said the backstop was “indispensable” to preserving political stability and the single market.
After visiting his counterparts in Paris and Berlin this week, Mr Johnson said there was “new mood music”, but reaching a new deal would not be “a cinch”.
He has insisted the UK will leave the EU on 31 October, whether or not a new deal is reached.
Mr Johnson will also meet with US President Donald Trump, who arrived in France around Saturday lunchtime.