United have been linked with a move for Huddersfield Town midfielder Lewis O’Brien over the past few weeks, but as it stands, Bielsa is not envisaging any incoming activity to bolster his squad.
Speaking before the Premier League home opener with Everton, he said: “It is not probable or likely that any more signings will be made.
“I am happy and comfortable with the players I have at the moment. It is the same group as last year with the substitution of (Junior) Firpo for (Gjanni) Alioski and the young players have had another year of experience.
“Of course, we have the option to bring another player in. As long as that player is able to challenge the player we already have in that position.
“But that means there is a very high cost. If there are signings below the level of the players we already have, there will be disappointment.”
Meanwhile, Bielsa says that England international and midfield talisman Kalvin Phillips is closer to a return after being an unused substitute in last weekend’s defeat at Manchester United.
But defender Diego Llorente will again be missing.
On Phillips, he said: “Another week of work means that physically, he is better and he is closer to being in the team.
“In this case, I did not think it was necessary.
And on the situation with Spanish international Llorente, he confirmed: “It is probable that he will have a chance to compete next week.”