He said tough negotiations within the European Council lie ahead, but chiefs must take leadership to show citizens they can make difficult decisions.
"It is clear to me that tough negotiations will be needed if agreement is to be found," Mr Kenny said. "Some headway was made at the European Council in November but considerable differences remain. From my contacts with colleagues, however, I believe that there is a shared appreciation that we need to close the deal this week."
The Taoiseach will travel to Brussels on Thursday for two days of discussions on the EU budget - known as the multi-annual financial framework (MFF).
European Council president Herman Van Rompuy, who will chair the talks, proposed a budget in November of around 972 billion euro for the seven-year period up to 2020. Chiefs in the European Commission had originally proposed to allocate one thousand billion euro.
"In setting out his assessment of how matters stand, president Van Rompuy has been clear that he believes further cuts will be necessary to bring everyone on board," Mr Kenny said. "A main part of our discussion will, therefore, focus on how big these cuts should be and where they should be applied."
The Taoiseach represented Ireland as EU president at a meeting with Mr Van Rompuy, European Commission president Jose Manuel Barroso and president of the European Parliament Martin Schulz earlier this week to discuss the MFF.
As current president of the EU, it is Ireland's responsibility to engage with the parliament to agree an overall seven-year budget. It will also manage around 70 pieces of legislation needed to implement the budget across the EU's many activities.
Meanwhile, President Michael D Higgins has insisted Ireland intends to make the most of its six-month presidency. He said the term offers the country a unique opportunity to contribute to the EU's development.
"We have a common purpose to create a social Europe and holding to that purpose, while working through our problems together, we will help our union - still young in historic terms - to emerge stronger and wiser," Mr Higgins said.