But Nato officials said the ministers would stop short of setting a target entry date at their talks in the Lithuanian capital Vilnius for fear of annoying Russia.
"Nato is an important forum for transatlantic dialogue on political issues; it is the premier forum," Rice said on Wednesday, after visiting Moscow where she criticised Russian President Vladimir Putin for having too much personal power.
But Russia will take part in the Vilnius talks on Thursday, and Nato officials said they saw Moscow as a partner.
The meeting in Lithuania, a former Soviet republic which joined Nato last year, underlines how the world has changed since the Cold War ended.
Nato has made it no secret that the victory of pro-Western Viktor Yushchenko in Ukraine's re-run presidential elections last December after a rigged first poll, had boosted the membership chances of Kiev, which also wants to join the European Union.
"The government in Ukraine has made its aspirations clear and is in a better position to fulfil its aspirations for reform," Nato spokesman James Appathurai told a news briefing, contrasting Yushchenko with his pro-Moscow predecessor.
Appathurai said 26-nation Nato would offer Ukrainian Foreign Minister Borys Tarasyuk a "form of enhanced dialogue, together with a package of practical and political elements".
The ministers would also offer Ukraine help to revamp its national army and pursue Western democratic reforms.
Pro-Russians are opposed to
Ukraine's closer ties with Nato
A senior US State Department official travelling with Rice said the Nato proposals were an "effort to move a little step further" in response to Ukraine's membership goal.
To boost Ukraine's entry chances, Washington wants Kiev to do more to fight corruption, exert more civilian control over its army and restructure its "top heavy" forces to reduce the number of generals, said the official, who requested anonymity.
There have been calls, notably in the United States, for Ukraine to be given Nato membership within five years.
But alliance diplomats fear a rush towards entry would not only raise tensions with Russia but alienate many Ukrainians in the former Soviet republic's pro-Moscow east.
Russian Foreign Minister Sergei Lavrov is due to sign an accord at the Vilnius talks codifying Nato troops' transit rights through Russia. This is seen as a step to make it easier for Nato and Russia to conduct joint exercises.
"Russia might feel it has reasons to be nervous about Nato. But Nato's message is that it wants to regard Russia as a partner," said one Nato diplomat, who requested anonymity.