Mary-Louise Parker and Jeffrey Dean Morgan in December
02/13/2008 AT 06:00 PM EST
On-again, off-again couple Jeffrey Dean Morgan and Mary-Louise Parker appear to be back on – as in, really
The pair are engaged, New York's Daily News
is reporting, saying that the two, who appear as husband and wife on the Showtime series Weeds
, have been telling friends of their intention to marry.
When reached by PEOPLE, a rep for Morgan had no comment on the report.
Morgan, 41, and Parker, 43, were first seen together at a party in New York in December 2006 and then went on to shoot down frequent reports
that they weren't getting along or had even parted ways.
Last March, they attended the opening night
of the Broadway musical Curtains
along with Parker's then-3-year-old son William – whose father is actor Billy Crudup, whom Parker dated from 1996 to November 2003.
In June 2007, Parker and Morgan really did split
("It just didn't work out," said Morgan, "wrong time in both our lives"), but by last December they were spotted together again
, this time at a movie premiere.
Asked that night what he thought about his date, Morgan told PEOPLE, "What about her?" as he raised an eyebrow and flashed a sly grin.
Not that son William and Morgan are the only ones in Parker's life. In September, her rep exclusively confirmed to PEOPLE that the actress had adopted a baby girl