"Arsenal away twice is a tough fixture for any team so really I guess they will be thinking everything starts from now.
"They will attack us and go for the win, but it's a game we're really looking forward to.
"The result will be whatever it is but we've got to make sure our performance is right, our attitude is right and the way that we play is right.
"I've got a group of players that are in the right frame of mind in that respect. We've got competition for places now, we're in a decent run and we want to keep that going."
Southgate was never an England regular during Keegan's turbulent reign in charge of the national team, which ran from February 1999 to October 2000.
In fact, the then Aston Villa defender started just six matches out of a possible 18, making a further three appearances from the substitutes' bench.
But the Boro boss has no hard feelings for Keegan.
He said: "I enjoyed my time with him at England and I think, though he didn't pick me all the time, if you work with somebody and they don't always pick you but you still have fond memories of that person then it tells you something about the relationship you had with them.
"He was somebody that I enjoyed playing for, somebody that made you feel you wanted to play for them and although we didn't have the most successful of times over that period, I thought it was a good camp to be involved in."
Keegan's continued enthusiasm for football comes as no surprise to Southgate, though he was surprised to hear he had been appointed Newcastle boss last month.
He added: "I was surprised because there hadn't been too much indication that he would take the job, but he's a football person and his enthusiasm for the game is immense so from that side of things it doesn't surprise me."