However, Rodgers has revealed that he remains confident of keeping Armstrong at the club after he played a key role in their Scottish Premiership title win last season.
The 44-year-old is quoted by the Daily Mail as saying: "We put the contract talks on hold. He's had the Scotland game and a holiday, so I'm sure they will resume over the course of the season.
"It's just negotiation. Stuart's at that point in his career. He had a brilliant season, he came on great strides last season.
"Contracts are always about length of time, or finances, but I am pretty confident the club and the agent will come to an agreement."
Armstrong has scored 23 goals in 103 appearances since moving to the Glasgow giants from Dundee United in January 2015.