Solanke signed from Bournemouth in a deal worth up to 65 million pounds ($85.47 million) but after making his debut against Leicester City he missed the next two games with an ankle injury.
Postecoglou will also have defender Micky van de Ven available again after he missed the defeat at Newcastle United before the international break.
"Micky is all good, he's trained fully over the international break. Dom (Solanke) is back with the first team, training today so again, we've got training tomorrow, if they get through alright, I guess they'll be available." Postecoglou told reporters.
Tottenham have had a mixed start to the season, picking up four points out of the nine available with a failure to convert enough of their 48 goal attempts in those games costing them.
"Results come sooner rather than later. We've got to stay consistent in our approach. We dominated all three games," Postecoglou, who is looking for his first win in the North London derby, said. "Results haven't come but if we maintain that over 38 games we'll be in a good position.
"We've got to keep at it. Stay focused on the important elements of our game."
Tottenham had marginally the better of the away clash with Arsenal last season, a game that ended in a draw, but lost 3-2 at home after trailing 3-0 at half-time.
Arsenal have re-emerged as Premier League title contenders under Mikel Arteta and Postecoglou said the Spaniard has instilled a relentless mentality in his squad.
"They have this confidence in themselves that they can challenge over the course of the season," Postecoglou said. "They're going to be a tough nut to crack, but it's a great opportunity for us."