The duo, who worked together on the film Terminator: Genisys in 2015, opted for a secluded restaurant during their meeting in London.
Sources close to the duo have also reportedly said the pair spent the night together and may be more than friends, fuelling speculation.
Matt had ended his long-term relationship with Lily James earlier this year. Doctor Who star Karen Gillan and model Daisy Lowe are also among those whose names have been mentioned together before.
According to reports, Emilia has also just ended her relationship with director and writer Charlie McDowell.