The striker has been linked with a number of clubs throughout January and previously after it was claimed he failed to secure the improved personal terms he wanted from Celtic.
Journalist Fabrizio Romano claimed Urawa had agreed a fee of about £3.5million with Celtic but Major League Soccer side Atlanta were still trying to sign the Greece international.
Reports in Japan have claimed Urawa are likely to sign the 28-year-old although personal terms have still to be finalised.
Giakoumakis scored Celtic's second goal in their 2-0 Viaplay Cup semi-final win over Kilmarnock on Saturday and posted a photo of his celebrations on Instagram with a caption that read: "Enjoy every moment like it's your last! On to the final.! Thank you for the immense support."
Giakoumakis has scored 26 goals since arriving from Dutch side VVV-Venlo 18 months ago, despite struggling with a knee injury in his opening months.
He has found regular starts hard to come by this season - his last came on November 5 against Dundee United - with his usual role being a substitute for Japanese striker Kyogo Furuhashi.