"Last year we spoke to the club and asked them if they wanted to do something and they said not.
"We haven't heard anything since, so that's where we are at.
"There are three things to it: availability, fitness and performance level. Hopefully I am delivering all three."
Per the report, the 33-year-old had been linked with a return to Leeds, but such a transfer stopped being feasible when they failed to win promotion to the Premier League. Fenway Sports Group, the Reds' owners, don't normally sign veterans over 30 to long contracts.
The versatile Milner has been a valuable member of the squad since joining in 2015, playing as both a midfielder and full-back. Last season, the vice-captain started 19 Premier League matches, and appeared in 12 more off the bench.
He showed no signs of slowing down and appears to have spent the summer working ahead of pre-season, rather than resting:
Manager Jurgen Klopp has spoken highly of him:
There's plenty of time left to agree a new deal with the veteran, who has perhaps done everything already to earn it and will have the chance to do so again when the season starts.
A move back to Leeds could also be tempting, however. Milner is from Yorkshire and spent his academy days with the Whites. He also made his Premier League debut with the club at the age of 16.
Leeds came close to Premier League promotion under manager Marcelo Bielsa last season, finishing the Championship campaign in third place. Derby County upset them in the play-off semi-finals.
If they do go one better and earn promotion this season, the addition of a Premier League veteran like Milner could be sorely needed.