The two countries have been embroiled in a diplomatic row since July 2008 after the brief arrest in Geneva of Moamer Kadhafi's son Hannibal when two hotel workers complained he had mistreated them.
The dispute escalated when Libya detained two Swiss businessmen, and Switzerland hit back by blacklisting 188 prominent Libyans from entering Europe's Schengen visa zone.
"We hope that Switzerland and Libya can sign on Tuesday a draft agreement on removing Libyan personalities from the Schengen blacklist and an act of clemency for the Swiss citizen still being held," said Frattini.
The two countries are to hold talks on Tuesday.
"Switzerland should understand that it is in its interest to find a solution," he warned.
Otherwise Ashton would "request" the Swiss remove the 188 Libyans, including Moamer Kadhafi, from the Schengen blacklist, said the Italian minister.
Italy has threatened it will no longer honour Switzerland's blacklisting of the Libyans after April 5, when new more flexible visa rules come into effect. Four others are also ready to take similar steps, according to an Italian diplomat.
The Swiss canton of Geneva has offered Hannibal Kadhafi compensation over the incident in an attempt to resolve the dispute, but Hannibal refused the offer.
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