Simon Hamilton was speaking on Thursday, after further talks aimed at resolving difficulties among the five parties resumed at Stormont.
Chancellor George Osborne has said corporation tax could be devolved if politicians resolve their differences over the budget and welfare reform.
Mr Hamilton said they had a "positive meeting" with Sinn Féin on Thursday.
"There was discussion around what agreement might look like, the sort of issues that we were talking about and where agreement might be reached on it," he told the BBC programme The View.
"It was certainly an advance on what has been happening in terms of the seriousness of discussions over the last couple of weeks.
"It actually has given me and the party some degree of hope that there is a prospect of a deal on these very difficult issues."
His comments come after Northern Ireland's First Minister Peter Robinson again warned that Stormont  could collapse if there was not a deal on the budget and welfare reform.
Mr Hamilton denied the party was sending out a mixed message.
"We could be on the verge of collapse if we don't redouble our efforts in a way that the two parties have committed to doing today," he said.
Daithí McKay of Sinn Féin said his party would prefer if the talks "were a lot more positive".
"There hasn't been an agreement as yet, we will continue to work constructively to reach agreement, but there's heck of a lot more to do," he said.
He accused the chancellor of "political blackmail" over the deferral of corporation tax.
Meanwhile, Deputy First Minister Martin McGuinness has tabled a paper at the talks calling for the creation of a Peace Investment Fund.
It is proposed the fund should be financed by contributions from the UK, Ireland, European Union and US.
Mr Hamilton, however, claimed his party was behind the move.
Northern Ireland Secretary Theresa Villiers has said the negotiations over the next few days would be crucial.
US envoy Gary Hart has also stressed the need to reach agreement quickly.
On Wednesday, Sinn Féin said it would not agree to the transfer of corporation tax to Northern Ireland "on the basis of implementing Tory policies".
First Minister Peter Robinson has blamed the delay in transferring powers on Sinn Féin and the SDLP's failure to agree a deal on welfare reform.
The Northern Ireland inter-party talks are aimed at reaching agreement on a range of unresolved issues, including disputes over flags, parades, the legacy of the Troubles and welfare reform.
The five main parties have clashed over welfare reform in recent months, with Sinn Féin and the SDLP objecting to many of the cost-cutting measures that have already come into force in England and Wales.
Unionists have argued that Northern Ireland must take difficult decisions to balance its budget, but nationalist and republican MLAs have said that many of the reforms will disproportionately disadvantage some of the most vulnerable people in society.
The DUP finance minister has said there is "some degree of hope" of a prospect of a deal in the cross-party talks.