Diane Wake, chief executive of the Dudley NHS Trust which runs Russells Hall Hospital, said guidance within the health sector says that existing methods of infection control would be sufficient in dealing with the strain.
Last week, Sandwell Council said there had been a probable case of the Indian variant found within the borough. There was also a case found in Tamworth, Staffordshire.
Asked about how the Dudley NHS Trust would deal with the Indian variant of Covid, Ms Wake told the trust's latest board meeting: "As far as we know, we haven't seen the Indian Covid variant in our hospital.
"How would we manage that? This is for any strain of Covid. It is about good infection prevention and control practices.
"It is about swabbing the patients on admission, to understand their status, isolating them appropriately. But maintaining, generally, within the hospital, good infection prevention and controls.
"That is social distancing, wearing of masks and different types of masks, depending on what type of patient you are caring for, and hand washing is so important.
"Whatever the variant, we would have those basic principles in place.
"My understanding through listening to organisations that have been dealing with this variant is it does appear to transmit more quickly.
"But we feel, and the mantra coming down nationally, is that it is the things we have been doing all along when we have managed Covid.
"That is good infection prevention and control, and swabbing patients appropriately when they come into hospitals, so swabbing patients on admission, day three, day five etcetera. We continue to do that. We currently have got nine inpatients in hospital. None of those patients are in critical care."
Board members of the Dudley NHS Trust have also heard how nurses are feeling under pressure.
Mary Sexton, chief nurse at the trust, said: "We have a very tired nursing workforce following the pandemic.
"We are doing lots to support their wellbeing but I still think that we probably haven't probably yet seen the full impact of Covid being played out through members of our workforce.
"I think that is something that all of us on the board are very mindful of and attuned to."