Speaking to the BBC, chief executive Gwendoline Cazenave said "bottlenecks" are beginning to appear in stations due to post-Brexit border checks and current levels of border staff.
The operator is currently running 14 services a day between the English and French capitals, compared with 18 in 2019.
Cazenave warned the company may not restore some services which were suspended last year due to the problems.
"The thing is now we are not able to run the same transport offer as what we had before in 2019, because of bottlenecks in stations," she reportedly said.
"We have a main issue in Eurostar terminals because of the new boarding conditions between the UK and EU; because of the impact of Covid; because of staff in the stations."
It comes as the firm unveils a new brand, with plans to carry 30 million passengers a year by 2030 across its Eurostar and Thalys brands.
