Stenny go into the clash with the capital outfit on the back of their first league win of the season last Saturday against Elgin City.
And McMenamin is anticipating another tricky encounter with City whom they beat 2-1 last Tuesday thanks to a double from Ryan Watters.
He said: “It’s another difficult game against Edinburgh City next week, we beat them 1-0 but it will be a completely different game.
“They’ll want a bit of revenge and they had a good victory as well at the weekend.
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“It’ll be a good game, everybody is much of a muchness I can’t see one team being far better than anyone else at the moment. We’ll work hard and see where it takes us.”
Stenny’s first league win in League Two came courtesy of Andy Munro’s second-half effort as the skipper led by example.
McMenamin said: “It’s a very good ball into the box and I’m just delighted that we have kept it alive and Andy’s in the right place to hit the target.
“We definitely deserved it, we probably should have scored another couple of chances on the break but we weren’t clinical.
“We’ve had a tough start to the season with the Betfred games and a couple of tough league games that were very difficult.
“We changed the shape about on Tuesday night and got a good win and then I think it’s the first time I’ve come up here and come away with any positive result, so I’m delighted with the way the boys worked and the play they did as well.”
McMenamin says he is still looking into strengthening the squad with the transfer window still open, he’s been without David Hopkirk through illness for the last week but he is expecting him to be back for the weekend as well as Aidan McIlduff.
McMenamin said: “Hoppy’s been ill but he text the boys in the group chat saying well done after the victory. He’s done well this season. He’s missed the last two games but he’ll desperate to get back for next week. It’s a good option for us.”