During a photo call on Friday, photographers asked the two world leaders to shake hands, but the President appeared to ignore both their and Ms Merkel's requests.
Ms Merkel can be heard saying: "Do you want to have a handshake?"
President Trump either does not hear the request or ignores it, continuing to sit angled away from her, hunched forward with his legs apart and hands together.
Photographers: Can we get a handshake?— David Mack (@davidmackau) March 17, 2017
Merkel (to Trump): Do you want to have a handshake?
Trump: *no response*
Merkel: *makes awkward face* pic.twitter.com/ehgpCnWPg7
Ms Merkel can be seen with a bemused expression on her face, clearly assuming she has been ignored.
President Trump previously slammed Merkel's immigration policies as well as criticising NATO and Germany’s position within the EU.
Ms Merkel, meanwhile, has led criticism of the President's travel bans.
President Trump and the German Chancellor did shake hands as she arrived at the White House earlier in the day.
They met in the Oval Office where they were expected to talk about strengthening Nato, fighting the Islamic State group and resolving Ukraine’s conflict.