Arsenal midfielder Coquelin is thought to be available in the January transfer window, and West Ham have been tipped as potential suitors.
“He would do okay for West Ham in that midfield area. He would do a decent job,” Parlour said.
“He’s not going to be an offensive player, he’ll be more defensive minded, but you might need that. He’s got experience, he’s played in big games, it wouldn’t be a bad signing.”
Coquelin has made 100 appearances for Arsenal over the course of his career, but he has failed to win over all of his doubters.
The 26-year-old has lacked discipline at times, but he would offer West Ham energy and dynamism in midfield.
West Ham are thought to be competing with Valencia for Coquelin’s signature, with interest rising in the midfielder.
Moyes is yet to make a signing in the January transfer window, but the Scottish boss is known to have money to spend at the London Stadium in the coming weeks.