When contacted by PEOPLE, the moving company, Wetzel & Sons, could not comment due to confidentiality.
The appearance of the van follows this week’s published account of a San Diego woman’s alleged tryst with Kutcher on Sept. 24, which was Moore and Kutcher’s sixth wedding anniversary, as well as recent rumors that the two are headed for a separation.
The couple, who began dating in 2003 and married in 2005, dealt with rumors of infidelity and marital trouble a year ago. At the time, they took a trip to Israel for what the actor described as a spiritual journey.
In her revelations this week, Sara Leal, who claimed a one-night stand with the Two and a Half Men actor, said he told her that he and Moore were already separated.
Representatives for the actors have not commented.