The couple, who recently got back together after separating last year, are said to be as happy as "love-struck teenagers," reported Radar Online.
The 68-year-old has asked Perlman, 64, if she would be interested in walking down the aisle for a second time to cement their union.
"Danny thinks it would be the ultimate in romantic gestures to renew his wedding vows with Rhea. He suggested it to Rhea, who wasn't against the idea, and told her it's something they should definitely consider.
"Rhea's not one to make a fuss, so she may say there's no need, but she does like the idea of being romanced by Danny all over again and is happy with the effort he's putting in to repair their marriage," a source said.