Allan Duckworth, chief executive of Burnden Leisure, which owns the club and the Reebok stadium, told the Bolton Evening News:
"Reebok has its European headquarters in the stadium, as well as the stadium naming rights and the club's kit sponsorship.
"From Reebok's perspective, this stadium is a shining light for the brand, and the set-up here is a picture frame for the brand in the UK.
"It is a very significant relationship. Both parties have got to be satisfied with a sponsorship deal or it won't work, and it certainly has worked very well over the years."
Duckworth said he saw no reason why adidas should change the relationship between Reebok and Bolton Wanderers.
He said: "It would not make sense to tamper with existing, successful brands. When you buy a brand, you are buying goodwill.
That is exactly what adidas is doing - buying goodwill, and there is every indication that they want that goodwill to continue."