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The Blues’ manager still wants to bring in a centre-back and will consider adding a midfielder, dependent on who becomes available between now and the end of the month.
But Tuchel says he will be happy to continue with no more additions after the club-record £97.5million signing of Romelu Lukaku.
After seeing his side continue their 100 per cent start to the season with Lukaku scoring in a 2-0 win against Arsenal, Tuchel claimed his squad was strong enough to cope if there are no more in-comings.
He said: “I am absolutely happy with our squad and the alternatives we have. It's not too big a squad, we were missing Christian Pulisic today and that meant everybody else was in the squad.
"That means we maybe don't have the biggest squad, but that we have a very competitive squad in all positions.
“This, on one hand, is necessary because we play a lot of competitions and we play the World Club Cup in December. We also played very long last season and there was the Euros and Copa America.
"So if we want to compete, we need this level. But at the same time, it's also important we're a strong group, this was maybe the key for the last half a year.
“We played with a strong bond and a great team spirit.
“This is a challenge for the team and for me to create this atmosphere again, and that everybody is ready to take hard decisions and keep pushing the team.
“If we do this we can achieve more than we have."