Published Wednesday, 16 July 2014
Some residents in the city claim the new building will obscure part of an iconic mural, which depicts the beginning of the Civil Rights Association and some of the people involved.
It was painted nearly 20 years ago and has become one of the most cherished.
Vinnie Coyle, whose late father Vincent is included in the mural, said: "It's hugely important to me because of my family links to this and the civil rights movement."
However he is concerned that plans to build an access ramp as part of a £2.2m extension to the museum next door will block at least half of the mural.
He continued: "It's a welcoming mural, we see it as being part and parcel of the museum experience which we all support, but we are against any obstruction of the view of this mural."
Management at the Free Derry Museum, which houses artefacts from Bloody Sunday, hope the expansion will accommodate the growing number of tourists visiting it.
They deny there has been a lack of consultation.
Adrian Kerr said: "We've had these plans in public for at least four years now, we've went round residents on a number of occasions and we've had public meetings.
"We've had a lot of publicity so we felt everybody was well aware of what our plans are, so we are a wee bit surprised that some people, a few people, weren't aware of what we are doing - but to say we are trying to damage the mural or block it off is completely wrong."
There will now be two meetings to discuss this issue held within days of each other.
The objectors will outline their concerns at a public meeting to be held next week while management will outline their plans at a meeting in the museum.
The public are invited to both as efforts continue to resolve this issue.
© UTV News