Ricardo Rodriguez has been linked with a move to Germany but Milan manager Gennaro Gattuso is determined not to lose the Swiss full back.
Rodriguez joined Milan from Wolfsburg for €15m last summer and he has been a regular at San Siro, under both Gattuso and previous boss Vincenzo Montella.
Both clubs can offer Champions League football next season whereas Milan only qualified for the Europa League, and they may yet be banned from that competition following a UEFA investigation into the club's finances.
Gianluca Di Marzio of Sky claims that Dortmund and Bayern have been in contact with Rodriguez's agent but have not yet contacted Milan about the possibility of a transfer.
Gattuso does not want to sell Rodriguez but the decision could be taken out of his hands by the club's hierarchy, who will accept an offer if it suitable for the player and the club.
New Dortmund manager Lucien Favre has worked with Rodriguez before, having coached him when the two were together at FC Zurich.
Bayern also have a connection to Rodriguez, as their Director of Sport Hasan Salihamidzic played alongside him at Wolfsburg.
Talks are nowhere near reaching a resolution yet and could continue well into the World Cup. Rodriguez's Switzerland kick off their campaign against Brazil on June 17.
Rodriguez was one of the breakthrough stars for Switzerland at the last World Cup and he made his 50th cap in last November's playoff win over Northern Ireland.