On Thursday the High Court ordered the payments to eight famous people, including ex-footballer Paul Gascoigne and actor Shane Richie. Payouts varied according to a number of factors including the number of hacks, stories published and the length of time.
In a statement to the stock market, Mirror Group parent company Trinity Mirror said the publisher "has already accepted that it should pay appropriate compensation to individuals who were the target of phone hacking".
"However, our initial view of the lengthy judgement is that the basis used for calculating damages is incorrect and we are therefore considering whether to seek permission to appeal."
The company said it is increasing its provision to deal with matters arising from phone hacking by £16m, in addition to the £12m it provided in 2014.
Writing for PRWeek, James Heath, lead solicitor for the claimants at Atkins Thomson, said the judgement "has been a good result for claimants, and they have finally been awarded what they deserve".
The majority of the damages awarded were six-figure sums, far higher than the settlement payments made by News International over phone hacking in 2013.
The publisher of the now defunct News of the World paid 15 people including actor Jude Law, former Labour deputy leader John Prescott and Welsh rugby player Gavin Henson a total £645,000.
The full list of damages awarded:
Sadie Frost - £260,000
Robert Ashworth - £201,000
Paul Gascoigne - £188,000
Lucy Taggart - £157,000
Shane Richie - £155,000
Shobna Gulati - £117,000
Alan Yentob - £85,000
Lauren Alcorn - £78,000.