The question mark hanging over the future of the Clark Clinic in Belfast is an issue which has united all political parties and representatives, according to Mr Farrell.
Its future has been placed in jeopardy following a recent Safe and Sustainable Review.
At a Public Meeting in Enniskillen last Tuesday night Fermanagh families who rely on the Children's Heart Services in Belfast pleaded for the facilities to be retained.
During his talk with Mr Wells at Stormont Mr Farrell highlighted the value in maintaining the life-saving services.
Describing the meeting as both "constructive and positive" Mr Farrell said the Health Committee vice-chair struck him as a man who was increasingly aware of the health and practical issues surrounding the issue.
"Whilst I certainly recognise there will be a need to have to travel on some occasions to Birmingham, we want to maintain the service here in Northern Ireland as well," he said, "I asked him to explore the possibility of a network model with Dublin. If it saves the services we have here in Northern Ireland, then it is certainly an option worth considering.
"I also impressed upon him that the service we have here is completely safe. The feedback from families in Clark Clinic is always very positive."
Mr Farrell also attended last Tuesday night's meeting.
"I felt it was an excellent meeting. There was a fantastic turn out from throughout Fermanagh and indeed beyond and I found it most touching to hear from some of the families whose children have been saved by the Clark Clinic.
"This service has given these people hope and we must do all in our power with devolved administration to save this it in Northern Ireland."