Reports in the Italian press have claimed Seedorf, who was only appointed in January following the exit of Massimiliano Allegri, is under pressure following a disappointing run.
Milan are without a win in their last five outings, leaving them languishing sixth in Serie A, although a 1-1 draw with Lazio on Sunday did bring to an end a run of four successive defeats.
Chief executive Galliani travelled with the squad to the Italian capital on Sunday at the request of Seedorf, who insists there are no hostilities between the pair.
"There has never been tension between us", Seedorf told the assembled media on Tuesday.
"Clearly when there are many outside influences, many things are believed.
"But the communication between me and Mr Galliani has been always for the good of Milan and we will continue that way.
"I work hard, I work for the good of the team, for results and I will never lose this."
Seedorf also revealed Galliani will be with the squad again on Wednesday when they travel to face Fiorentina in Serie A.