Gregory, who took over as Crawley boss in December last year, had endured a dreadful season with the West Sussex club.
Crawley have won just five League One games this term and sit 21st in the English third tier as a result.
A 4-1 defeat to Leyton Orient on Friday marked their 10th league loss of the campaign, with Gregory stepping down a day later for health reasons.
The former Aston Villa manager is scheduled to undergo open heart surgery in early January, but is expected to return to Crawley when he has recovered.
Ex-Doncaster Rovers and Wolves boss Saunders has come in on an interim basis, and will look to end Crawley's 10-game winless run against a Colchester side who sit two places below them in the relegation zone.
Bottom club Yeovil Town take on Leyton Orient on Monday in another big fixture at the wrong end of the table, and 22nd-placed Crewe Alexandra will look to build on their 2-1 win over Oldham Athletic when host promotion-chasing Preston North End.
Preston are in a group of four teams separated by just a point at the top of the table, with Bristol City holding a slender edge over the chasing trio.
City travel to Gillingham looking to maintain their position at the summit, while MK Dons and Swindon Town - ahead of Preston on goal difference - meet Walsall and Port Vale respectively.
In-form Bradford City host Notts County aiming to extend their unbeaten run in all competitions to nine matches.
By contrast, Yorkshire rivals Sheffield United meet Scunthorpe United hoping to arrest a slide that has seen them go six league games without a win.
Elsewhere, Coventry City face Chesterfield, Peterborough United take on Doncaster Rovers, Rochdale welcome Fleetwood Town to Spotland and Oldham visit Barnsley on Monday.
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