The towers are covered in high pressure laminate (HPL) cladding which the government has advised should be removed from high-rise buildings.
Watkin Jones said it would look to recover some of the costs from consultants and subcontractors involved in the original construction.
It said: “In response to the revised Government guidance, issued in January 2020, on the suitability of certain cladding solutions used on high-rise residential buildings, the Group is working with the owners of eight of its previously developed purpose-built student accommodation schemes to remediate/replace cladding.
“The majority of the cladding is high pressure laminate (HPL), which has been under more recent scrutiny and is covered by the revised guidance.
“The group is taking proactive and responsible steps to ensure the safety of tenants, working with building owners, even though the buildings concerned were developed in accordance with all building regulations at the time of construction and no liability is accepted for the works.
“Discussions with the property owners remain ongoing, but the board currently expects that this may result in a sharing of the costs of certain remedial works with them.
“The gross cost to the group could be in the range of £12 million to £15 million, over the next two years.
“A one-off non-underlying provision for this cost is likely to be made at the year end, once the outcome of those discussions has been established.
“The group will look to recover some of this cost from the subcontractors and consultants engaged on implementing the particular cladding systems at the time.
“This is likely to take an extended period of time to achieve and the extent of any recovery is currently uncertain.”
The announcement came at Watkin Jones announced strong first half results for the six months to March 31 2020.
Pre-tax profit was up to £26.6m from £22.4m last year as revenue rose to £185.7m from £159.1m.
Most sites have now been remobilised following lockdown with jobs operating at around 75% capacity.
Watkin Jones said: “We anticipate a modest increase in costs to complete our committed development programme during Covid-19 disruption.”