Relegation-threatened Livorno have sacked Domenico Di Carlo after just 88 days in charge and re-appointed Davide Nicola.
Virgil van Dijk claims he knows nothing of interest from English clubs and is keen to prove himself in the Champions League with Celtic.
Kiwomya joined County in February 2012 as their development squad manager and has been in charge of the first team since February this year following the departure of Keith Curle.
On their website the club said "despite playing an attractive and exciting style of football" it was decided the two parties would "part company".
County lost 1-0 at home to Preston on Saturday, leaving them bottom of Sky Bet League One, with just two wins from their opening 13 matches.
"I cannot express how difficult a decision that this has been for the board of directors," chief executive Jim Rodwell said.
"This has been a grueling year for Chris, both on the pitch and personally. Chris has conducted himself with dignity and professionalism throughout.
"We would like to state, for the record, that we continue to hold Chris in high regard. His work-rate, enthusiasm, commitment to the club and importantly, honesty and integrity are commodities rare in football today,"
Assistant manager Mick Jones and first-team coach Andy Watson have also parted company with the club.
Development squad manager Steve Hodge will take charge of the first team for Tuesday night's league game against Oldham and he has been installed as favourite to take over on a permanent basis by Sky Bet.