It's a difficult task. One of the leaders of last year's Orange Revolution -- Yekhanurov's predecessor, Yuliya Tymoshenko -- has been fired from her job. The economy shows no sign of recovery. Even worse, economic growth has slowed from an annual rate of 12 percent in 2004 to less than 5 percent this year.
Yekhanurov has made reviving the economy his main priority. But he has to convince the EU that Ukraine is serious in its intentions, and that market reforms will begin in earnest.
Oleksiy Kolomiyets is the head of the Kyiv-based Center for European and Trans-Atlantic Studies. He said the visit may be crucial in infusing new life to Ukrainian-EU relations.
"The main point in the discussions will be to find some way to give an impulse in achieving the aims which were outlined in the action plan," Kolomiyets said.
The EU and Ukraine signed a three-year action plan in February, just after the Orange Revolution brought Viktor Yushchenko and his allies to power.
The plan aims to bring Ukraine closer to the 25-member European bloc by setting out the main areas of reform the country needs to implement to meet EU standards. The areas range from democratic safeguards to steel import quotas and a relaxed visa regime.
Kolomiyets said almost nothing mentioned in the action plan has yet been implemented because of a lack of will, infighting, and scandals.
Stuart Hensel of the London-based Economist Intelligence Unit said the EU already feels disappointment with the way things are going in Ukraine. He said recent corruption scandals involving government officials had a sobering effect in the West.
"There was definitely quite an awareness in the EU of the seriousness of the corruption allegations that were made and of the knowledge that many of the problems continue, and I think it has a sobering effect on some of the perceptions of Ukraine in the EU," Hensel said.
Hensel said it is more difficult to overcome the legacy of former President Leonid Kuchma than it was believed during the heady days of the Orange Revolution.
On 5 October, the Council of Europe adopted a resolution, which takes a more realistic look at the country.
The resolution criticizes Ukraine over slow progress in implementing political, social, legal, and economic reforms. It says Yushchenko has fallen short of his own goals since he took office in January.
The council is especially critical of the high degree of corruption and widespread human trafficking in Ukraine.
The document singles out deep political divisions as leading to the governmental crisis, and says there is a lack of media pluralism and freedom of the press.
However, Ukraine needs more than good advice.
Yekhanurov wants the EU to support Ukraine's application to join the World Trade Organization (WTO), which Ukrainian officials say can help push forward economic reforms.
Hensel said it is unlikely the EU support will be enough.
"I think lot of the decisions still need to be taken," Hensel said. "However, they are really not under EU's control, I think. A lot depends on what other countries, particularly the U.S., decides to do."
In Brussels, Yekhanurov will also meet with officials from NATO.
Kolomiyets said relations with NATO should also be pursued more energetically, and need to go beyond declarations to concrete actions.