Mertesacker left Werder for Arsenal last week.
Allofs told Kreiszeitung Syke: "Per Mertesacker always said he would have loved to remain with us. I trust him, he is simply an absolute honest character.
"But he also said he would love to join Arsenal now. This is why we then started to negotiate a deal.
"We were not taken by complete surprise as you could foresee such a bid. We agreed with Arsenal FC on Tuesday, these negotiations went quickly. We are delighted with the deal."
Allofs added: "I believe Per Mertesacker is a good fit, he will do well in the Premiership. He will break through. It's obvious his game needs a bit of adopting to that standard there. But he is an intelligent player, he will do so."