Glenfield Hospital claims up to 150 patients a year from the East Midlands were sent to centres further away.
NHS England said the hospital's three surgeons are not meeting a total target of performing 375 operations a year.
Many patients from Northampton and Peterborough are transferred to Great Ormond Street Hospital (GOSH), London.
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In 2016, Glenfield Hospital operated on 328 children and hopes to carry out about 350 this year.
Figures obtained by the BBC in a Freedom of Information request showed that on 29 November 2016, GOSH had 159 patients on its waiting list.
Some other hospital's had about 70, while Glenfield had 14 children waiting for surgery.
Dr Aidan Bolger, head of service for East Midlands Congenital Heart Centre, said referring patients would be a "simple solution" and closing the service "wouldn't be necessary".
"This is a proposal we've put to NHS England," he said.
Northampton General Hospital, which is about 45 miles away from Leicester, said for the past five years it has referred up to 25 children a year to GOSH, which has been "approved by NHS England".
Peterborough and Stamford Hospitals NHS Foundation Trust said: "The foetal echo service provided by Great Ormond Street Hospital... is the key reason that most children with congenital heart disease in Peterborough are seen there."
A spokesperson for GOSH for Children NHS Foundation Trust said it "accepts referrals from across England".
NHS England said: "We will not dictate referral patterns that would take choice away from patients and their doctors."
No decision has been made about the future of children's heart surgery at Glenfield Hospital - a consultation ends in June.
Children's heart surgeons in Leicester have said their service could be saved from closure if more patients from the region were referred to them.