Cable TV broadcaster NTL plans to transfer up to 70 jobs from its base in Coventry to other locations in the UK.
NTL said the job move would improve customer relations
The company said it was consolidating customer relations jobs at three other centres in England which would significantly reduce operational costs.
The company said no redundancies would take place with staff being redeployed elsewhere in the organisation.
NTL pledged its future to the city. It recently merged with rival Telewest making 6,000 job losses nationally.
Two hundred and fifty people work at the telecoms company's headquarters in Hertford Street.
The firm told the BBC it is consolidating its customer relations activities at three sites in Manchester, Gateshead and Sheffield.
It said the changes would allow the company to simplify and improve its customer experience so that more customers would recommend it, as well as cutting costs.
It has started consultations with staff over the changes.