|Moore and Morton|
A source told People.com that 'The Joneses' star and the restaurant owner - who dated Lindsay in 2006 - have enjoyed several dates recently and seem really into each other.
The insider said: "Demi was very giddy during her date with Harry. She was really into him and seemed to very much enjoy his company"
The couple were spotted having dinner together in the South Beverly Grill in Beverly Hills and have also been hanging out at Demi's mansion nearby.
An insider told E! News: "They are just getting to know one another... (Demi is) in a really good place at the moment and is hopeful about the future."
Demi's new romance comes just weeks after she split from her toyboy lover Vito Schnabel.
The 26-year-old art dealer broke off their relationship last month after he became concerned that the attention surrounding their relationship would distract from his career.
Harry was previously linked to Jennifer Aniston, whom he reportedly dated briefly in 2010.
Meanwhile, Demi's divorce from Ashton Kutcher has stalled over money.
The former couple called time on their marriage in November 2011 but Ashton only filed divorce papers last month and reports suggest they cannot agree on a settlement.
A source previously said: "The sticking point in the divorce has been that Demi wanted the same type of settlement from Ashton that she got from Bruce Willis."