The pair, who star together in the upcoming film The Naked Gun,  have been spotted sharing affectionate moments during their press tour,  including a playful kiss on the red carpet and flirty exchanges on the Today show.  A source close to the couple describes their relationship as "sincere," noting that they're "enjoying each other's company." 

Their connection reportedly blossomed during filming,  with Anderson baking sourdough bread and cookies for Neeson, and  Neeson praising her as "terrific to work with."  The couple made a public appearance at the New York City premiere of The Naked Gun, accompanied by their children, signaling the seriousness of their relationship.