The 49-year-old manager was dismissed by the West Ham board on Monday, after losing 4-1 to Liverpool on Saturday evening in the Premier League and dropping into the bottom three of England's top tier.
Plenty of names have been thrown about since Bilic's sacking on social media, with former Everton and Manchester United manager David Moyes leading the way to be announced as the new manager of West Ham.
However, Ashton claimed in a video posted on his personal Twitter account that he would not consider Moyes, and instead would look at bringing Alan Pardew back to east London. He also gave his opinion on Roberto Mancini and Ronald Koeman.
"Moyes? Not for me, really," Ashton said. "I don't think his style of football and his mannerisms are going to excite West Ham fans. For me, I think Pardew has got to be a contender.
"He's been at the club, I've played under him. He would get a response from the players and play attacking football, which is what we want to see. He has got good experience, especially since the last time he was at West Ham.
"Mancini is another one; people would be excited, but it's a different proposition here. Ronald Koeman would also be another I'd look at. At Southampton he did a fantastic job, you don't become a bad manager after one spell."
West Ham fans let me know who you want as next manager?— Dean Ashton (@Dean36ashton10) November 6, 2017
i would bring Alan Pardew back! pic.twitter.com/P4VV7vMlzH
Pardew, 56, has been out of work since being sacked by Crystal Palace in December 2016, but has been linked with a multitude of jobs since leaving Selhurst Park.
He worked for the Hammers for three years between 2003 and 2006, helping them achieve promotion from the Championship to the Premier League n 2004-05 before guiding West Ham to ninth place and an FA Cup final the season after.
Former Man City boss Mancini is currently in charge of Russian giants Zenit St. Petersburg, while Koeman is also out of work after being sacked by Everton last month.