Reports in Italian media say the 37-year-old coach is under pressure for poor results and his team's style of play. They visit Lazio on Sunday before travelling to Florence.
After a meeting in Milan on Friday it emerged that chief executive Galliani will be following the team to its pre-match training camp to "tutor" Seedorf.
"It (the meeting) was a request that was made of me two days ago," Seedorf told a news conference on Saturday.
"I rearranged training to be able to make the meeting and speak with Galliani about everything. It was constructive.
"I asked him to stay close to us, as we agreed before I signed as manager, because I didn't come here thinking I could do it all by myself.
"With all the experience Galliani has I'm very happy that he decided to stay closer to me and the team, because the club has always been strong in moments of difficulty, and right now I can see that."
Milan have lost seven of 12 matches since Seedorf was appointed manager in January. They were knocked out of the Italian Cup by Udinese and humbled 5-1 on aggregate by Atletico Madrid in the Champions League.
They are 11th in Serie A on 35 points, 12 behind city rivals Inter Milan in fifth. They are as close to the relegation zone as they are the European places.
There have been reports that Seedorf will be replaced by deputy Mauro Tassoti until the end of the season, before youth team coach and former Milan striker Filippo Inzaghi takes over in the summer.
After last week's 4-2 defeat to Parma, a delegation of hardcore "ultra" fans demanded to speak to Seedorf. It is the latest in a long line of protests in a wretched season for Milan, who were once giants of the world game.
"I've not heard anything from the club regarding my position. Before I signed I said I would be here to do the best I could with this season and then build for the future, so until I hear something from the club that's how it will stay," Seedorf said.
"I'm convinced the team will do better, that the results will get better. We all - me, the players, the club - want to improve results and we're working together to do that."
- Sports & Recreation
- Inter Milan