The 33-year-old midfielder joined Rangers on a Bosman back in May but the Premier League veteran has barely trained with the Gers as of yet.
The former Newcastle United and Manchester City man missed the club's pre-season trip to the United States and has only began training with his new team-mates this week.
Consequently, Barton is likely to be quite a bit behind his Rangers colleagues in terms of overall fitness, and Warburton does not expect him to figure on Saturday.
Barton was Warburton's second summer signing as the outspoken midfielder followed Jordan Rossiter to Ibrox, the 19-year-old joining on a £250,000 compensation deal from Liverpool.
However, the young midfielder is on international duty with England Under-19s, and he too will miss the visit to Fir Park for what will be Rangers' first League Cup game in the space of nine gruelling days.
“Saturday might be too soon for Joey. Jordan Rossiter is away with England's under-19s so he won't be back till after that. It will depend on how they get on," he said via The Glasgow Evening Times.
Rangers have only had one pre-season friendly so far - a 2-1 win away to Charleston Battery on their trip to South Carolina.