"We've discussed that, we are hoping very much that a visit can be arranged as soon as convenient but no date has yet been fixed," Foreign Secretary Jack Straw told a news conference in London after landmark talks with his Libyan counterpart.
Earlier, Libya's foreign minister Muhammad Abd al-Rahman Shalgam began a landmark two-day visit to the United Kingdom, marking the diplomatic rehabilitation of the one-time pariah state.
No Libyan foreign minister has visited Britain since 1969, the year al-Qadhafi took power in a bloodless coup.
The British Foreign Office has called the visit a "milestone in what have been steadily improving relations" and part of a wider plan to bring Libya into the "international mainstream".
Libya has long been listed by the United States as a sponsor of terrorism and suffered UN sanctions until last year for the 1988 bombing of an airliner over Lockerbie, Scotland.
But London and Washington have been moving rapidly to bring Tripoli back in from the cold over the past several months.
Last year, Libya paid a $2.7 billion compensation package for Lockerbie victims before making a surprise declaration in December that it was dismantling banned weapons programmes.
Al-Qadhafi pledged in December
to end quest for nuclear arms
Britain has moved somewhat faster than the United States to restore ties. Washington has yet to lift economic sanctions, including a ban on travel by US citizens to Libya.
Those sanctions are keeping lucrative oil deals on ice.
But after three-way talks in London last week, US officials said they had discussed loosening the sanctions.
Meanwhile, Italian Prime Minister Silvio Berlusconi arrived in Libya on Tuesday on the first visit by a Western leader since Libya announced in December it was halting plans to develop weapons of mass destruction.
Berlusconi flew from Rome to Libyan leader al-Qadhafi's home town of Sirte, where he was greeted by Prime Minister Shukri Ghanim, local officials said.
Government officials and diplomats said the two leaders would discuss joint efforts to stem the flow of illegal migrants from Libyan shores across the Mediterranean.