The c.1297 picture of Madonna and Child is in storage in London and was exported to the UK from Italy in 2007 following litigation in the Italian courts.
Dealer Kathleen Simonis later applied to the Arts Council for a licence to export the painting out of the EU, which was refused in 2015.
The Arts Council maintains that it is unable to grant an export licence because the Italian authorities say the painting did not have the necessary licence to be exported from Italy in 2007 and are seeking to have it returned.
Barristers for Simonis argued that an export licence was not required in 2007 following the Italian litigation.
The court case, which was heard on June 28, involves Simonis and the Arts Council.
According to reports of the trial, Simonis paid 8m lira - around £3500 - for the painting at auction in 1990 when it was believed to be a 19th century copy.
But, during restoration work in the late 1990s, layers of paint were removed to reveal the work of the Florentine master Giotto (1267-1337) and it was re-attributed and is now valued in the region of £10m.
Simonis has taken the painting out of Italy on a number of occasions under a temporary Italian licence while being the subject of litigation in the Italian courts.
Simonis is represented by Aiden O’Neill QC. Ben Jaffey QC is acting for the Arts Council.
The court reserved judgement which will be handed down in due course.