The 25-year-old Japan international, who spent two disappointing seasons at Manchester United after winning back-to-back German league titles at Dortmund in 2011 and 2012, scored one goal and helped set up the other in their 3-1 win over Freiburg.
"For a first game back it was an extraordinary one for him on Saturday," Klopp told reporters. "We saw the opportunity and used it to bring him back and at least here everyone is happy."
"A decision whether he will play tomorrow will be taken tomorrow morning."
Kagawa, a crowd favourite in Dortmund, instantly added pace and creativity to their game, especially with a handful of midfielders missing through injury, including Marco Reus, Nuri Sahin, Jakub Blaszczykowski and Ilkay Guendogan.
Another player itching to get match practice is Sven Bender, who missed the World Cup through injury and looks fully fit after coming on as a substitute on Saturday.
He could replace Serbian holding midfielder Milos Jojic, who did not look sharp against Freiburg.
"Sven Bender is an option for tomorrow," said Klopp, who added a decision on Jojic would also be taken on Tuesday morning.
Dortmund played Arsenal in 2011 and last season when they lost 1-0 at home but beat Arsenal in London 2-1.
"Those who saw Arsenal here last year know very well they can also play defensive football and switch their game very quickly.
"So we should play according to our most natural virtues and take some tactical measures to keep them at bay."
(Reporting by Karolos Grohmann; editing by Clare Lovell)
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