The 30-year-old drew with Wilder in Los Angeles on Saturday in his bid to win the WBC heavyweight title from the American.
Manchester-born Fury was in attendance at Old Trafford as Manchester United drew 2-2 with Arsenal on Wednesday in the Premier League.
Speaking to BT Sport, he said: “Frank Warren (his promoter) said Arsenal but I said ‘No, let’s have it at Old Trafford’. Hopefully we can have it here in the summer.”
Fury was denied one of the greatest comebacks in boxing history after scores of 115-111, 112-114 and 113-113 over the weekend.
He impressively out-boxed the champion, although Wilder retained the title having knocked the Briton down in the ninth round, and again in the 12th.
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