The 25-year-old was signed in a £47.5 million deal from RB Leipzig last summer but has struggled in his first season at Stamford Bridge with 10 goals in 37 appearances.
Earlier this week, pitch-side microphones caught Tuchel tearing into Werner over his poor positioning during Chelsea’s win over Everton.
The Germany international was subsequently dropped for Chelsea’s trip to Leeds United on Saturday.
And Merson believes Werner’s place in the team is now under even more threat with Kai Havertz finally showing signs of improvement under Tuchel.
Asked if he believes Tuchel is running out of patience with Werner, Merson told Sky Sports: ‘I think so, and I think even more so after the way Havertz played last week, I thought he was absolutely outstanding.
‘He came into the No.10 position and I thought he was absolutely outstanding.
‘If you’d have said to me three months ago that Havertz is that quick I’d have said I haven’t seen it. But I saw it last week.
‘It just shows you he’s a confidence player, he looked very good.
‘I think with the way he played he will lose patience with Werner.
‘There’s a lot to work on, I think he makes bad, bad decisions too many times in football matches. And when you’re costing that kind of money that shouldn’t really happen.
‘Havertz, I think, was absolutely outstanding. You’ve got Mount to come back, who was out of that game and he’s played his best game against Liverpool.’