Speaking in Algiers, Mr Annan said he was in contact with the Libyan Government, and "might go" to Libya when he ends a visit to Tunisia.
In fact it is assumed he will go - and, possibly, seal arrangements for Abdel Basset Megrahi and Lamen Khalifa Fhimah to face trial at a court in The Hague.
With the 10th anniversary of the destruction of PanAm's flight 103 just 18 days away, the Foreign Office is bending over backwards to avoid any impression of a deadline.
Only too aware of Mr Gaddafi's proven capacity for stalling, officials in London merely express encouragement at the "serious engagement" of the Libyans in seeking a resolution of the issue.
Exactly what Mr Annan will do in Tripoli is unclear.
If the end game is at hand, he would be expected to confirm that, once the suspects had been surrendered, the UN's sanctions against Libya would be lifted.
But during a phone conversation last week with Mr Annan, the Foreign Secretary, Robin Cook, made it clear that there could be no negotiation.
The ball, Britain insists, is firmly in the Libyan court. The hope is, as one official put it, "that Annan's going there will be a peg for Gaddafi to make an announcement."
But the Libyan's intentions are as mysterious as ever. Years of total deadlock were broken in August when the US and Britain, fearful that UN sanctions aimed at isolating Libya were slowly dying by default, abandoned their long standing insistence that the two men's trial be held in Scotland or America.
In return, Tripoli seemed to agree in principle to hand over the suspects.
Nonetheless, prevarication over the details had continued, before the waters were further muddied last week by reports from Tripoli of the trial and imprisonment of three senior Libyan security officials, allegedly on the grounds of "dereliction of duty" over the bombing, in which 270 people were killed.
That step was interpreted in some quarters as a sign that the crucial breakthrough was at hand, and that by jailing three key witnesses who would otherwise have been called to testify in The Hague, the Libyans were seeking to make it hard, if not impossible, to convict Megrahi and Fhimah.
Other analysts however maintain that the three - one of them the brother- in-law of Mr Gaddafi himself - are so senior that their belated "imprisonment", if such it is, may presage a definitive refusal to deliver the two men accused by the West of actually planting the suitcase bomb which blew the PanAm Jumbo jet apart.
According to this theory, the Libyan president would argue that the individuals who had plotted the crime had been punished and justice done, so that no grounds any longer existed for a trial of the mere foot soldiers in Britain's worst ever terrorist outrage.Reuse content