Rinne made the remarks while speaking to reporters after a meeting with the French President here on Wednesday, the BBC reported.
"We both agreed that it is now time for (UK Prime Minister) Boris Johnson to produce his own proposals in writing - if they exist. If no proposals are received by the end of September, then it's over," he said.
The Finnish Prime Minister added that he intends to discuss the new deadline with the President of the European Council, Donald Tusk, and Johnson in the coming days, but the position has not yet been agreed with other European Union (EU) nations.
Finland currently holds the EU's rotating presidency.
Reacting to Finne's statement, a Downing Street source said: "We will continue negotiating and put forward proposals at the appropriate time."
Johnson has said that a deal was possible at a crucial summit of EU leaders on October 17, but has insisted that Brexit will happen by the October 31 deadline, with or without a deal.
The UK government said talks with the EU have been making progress since Johnson became the Prime Minister in July.
The government said that it had put forward "a number of proposals" as alternatives to the Irish border backstop - the policy aimed at preventing the return of a hard border on the island of Ireland and a key sticking point in former Prime Minister Theresa May's Brexit deal.
The EU has continued to criticise the UK for not putting any plans in writing, reports the BBC.
Earlier, European Commission President, Jean-Claude Juncker, said a meeting with Johnson on Monday had been "constructive".
But he said until proposals had been put forward, "I will not be able to tell you, looking you straight in the eye, that any real progress has been achieved".
( With inputs from IANS )