This summer window has included a record-breaking deal for Spanish international forward Rodrigo from Valencia and the capture of defenders Robin Koch and Diego Llorente.
Bielsa had said they wanted to try and bring in two more players and Leeds came close to getting a midfielder this week before a move for Bayern Munich midfielder Michael Cuisance broke down at the last minute due to concerns arising from his medical.
Leeds have until 11pm on Monday to complete deals for players playing abroad and Premier League targets, but a domestic window for business between Premier League clubs and EFL outfits will remain open until 16 October.
Kinnear wrote his programme notes for this evening's clash with Manchester City before the drama surrounding 21-year-old Cuisance unfolded but suggested there could still be a new face or two before the deadline.
If Leeds don't sign anyone, however, they're content with what they've done in the window because their chief aims of strengthening the first team and bringing in top youth prospects have been met.
"At the time of writing (Wednesday morning) there are still one or two potential pieces of business to be done but even if they are not completed, we are confident in the squad we have assembled," said the chief executive.
"Our 12 summer signings to date have delivered on our objectives of: one, solidifying the core of the team that served us so well last year; two, adding the quality of proven internationals who can immediately contribute to the first team; and three, securing some of the highest potential youth players in Europe.
"Crysencio Summerville was the latest addition on this front and - like his fellow Under 23 team-mates Joe Gelhardt, Sam Greenwood and Cody Drameh - we believe he will be pushing for inclusion in the first-team squad before the end of the season."