The 28-year-old became the top scorer for his nation after scoring in the 1-1 draw against Germany on Thursday.
"I think he loves playing for his country, this is the last swansong before he has a little bit of a break and then obviously he will decide where he's going to go," Dixon said on ITV.
"There are a lot of question marks 'is he going to stay at Arsenal?' or 'is he going to move on?'.
"He will put that to the back of his mind and he's a great player to watch, he really is."