The Steelmen are sitting in fifth place after a largely excellent opening half of the season, but second placed Celtic are rampant just now as they vie with Old Firm rivals Rangers for the title.
Alexander, whose team visit Parkhead on the back of drawing 1-1 against Hibs at Easter Road last Saturday, said: "We're under no illusions about the type of challenge that's coming our way on Sunday, it's a big one. As they all are, but we're looking forward to it.
"It's the chance for us to see how much we've improved - certainly in the last month - because it's one of the sternest tests you're going to face, as a Scottish Premiership club.
"We have to go and try our best to get a result.
"We go into it with a lot of confidence. I think our form has been good over the last month, but there are a couple of things we need to try and improve.
"I thought we dropped below it just a little bit last week in the Hibs game, but we know there are going to be little bumps along the way in different challenges we face, and opposition looking at what we do and trying to overcome it.
"That's the nature of the game, but we're constantly evolving, trying to be a better team each week - but you get a really good indication of how much you're improving, or where you are, by being challenged every single week by good teams.”
Alexander insisted it’s not just Celtic’s front three who will cause a threat to his side.
He added: “They've got talent all over the pitch and all over their squad, because they can miss players and still bring in top quality players.
"We have to focus on how we get our game going, on them as a whole, because their success and results have certainly not just been down to one, two or three players, it's a collective, and they've got a lot of talented players.
"The challenge we face on Sunday is not just from certain individuals.”
At least Motherwell have Tony Watt – the Premiership’s top scorer this season with nine league goals – in their ranks.
Alexander said: "Tony has done great this season with his goals, but if you look at the other forwards we have in the squad, they've got as much talent and goal-threat as him.
"He's hitting the target more often than not, and getting those goals with some quality finishes, but we know we've got that goal threat in numerous players and we have to always carry that.
"We always have to carry that puncher's chance of winning, and we know when opportunities fall to these players they're going to have to hit the target.
"We understand that we're going to have to get our defensive game really sharp, but we always have to carry a threat of our own or there's no point in taking part in the game."