Caithness civic leader Gail Ross called for its end last year after local people raised concerns about Klaksvik's use as a whaling port.
Civic leaders in the Faroese city responded by saying the whale hunting was done sustainably.
Next week, Highland Council's Caithness Committee will be asked to discuss formally ending the twinning link.
Options councillors will be asked to consider also include leaving the twinning status as it is.
In a report to Wednesday's meeting, council officers said contact between Wick and Klaksvik had been "limited" for several years.
They said the last formal visit took place in 2001 and fishing links between the two places were no longer relevant because Wick was not now a designated fish landing port.
Highland councillors are to consider breaking a twinning link between Wick and Klaksvik in the Faroe Islands.