Fernandes has been tipped to join United throughout the transfer window and talk of a switch to Old Trafford has gathered pace with the Premier League season on the horizon.
The Portuguese Super Cup – which Sporting lost 5-0 to rival Benfica – was widely seen as a potential Fernandes farewell before leaving Lisbon.
Portugal international Fernandes was a topic of conversation post-match and Keizer told reporters: "Bruno Fernandes is an important player.
"Will he stay? It's not a question for me, but for the management."
Fernandes scored 20 goals – 31 in all competitions – and supplied 13 assists in the Primeira Liga last season as Sporting finished third.
The 24 year-old played the full 90 minutes as Sporting was humiliated by Primeira Liga champion Benfica.
Pizzi scored a brace, while Rafa Silva, Alex Grimaldo and Chiquinho were also on target against Sporting, which had Idrissa Doumbia sent off in the 89th minute.
"It's a night to forget," Keizer said. "We had a good chance to score, but we couldn't. We never gave up trying to score even after we were losing by two and three goals. Benfica also created a lot of chances and managed to score.
"It will be a very difficult week, but we have a match for the championship next week and we have to prepare it."
Keizer's Sporting opens its league campaign away to Maritimo.