Aberdeen face Celtic at Pittodrie on Saturday with a club record-equalling 100% start to the season.
The Dons will be looking to improve on last season’s showing against their main rivals for the title, when they lost all four matches with the Glasgow team.
Those matches were the difference between first and second in the SPFL Premiership and left manager Derek McInnes and his players disappointed despite recording their highest finish in the top flight since 1994.
Legend Miller, who scooped three top-league titles with Aberdeen, says they can challenge again this year - and Saturday will go a long way to discovering how close it will be at the top.
He told Sky Sports: “Aberdeen made a valiant effort of it last season. They kept it going until April and fell away towards the end of the season.
“They have strengthened their squad as well, are playing some good football and have got a lot of experience. If you are looking around the game then the challenge should come from Aberdeen.
“Whether they can lift themselves to overcome Celtic is another matter but I think they will make it difficult again this season.”