Ronny Deila’s men will meet the Swedes in the play-off round for a place in the group phase of the competition.
Celtic have so far defeated Icelandic side Stjarnan and Azerbaijani title holders Qarabag to progress to the last preliminary round.
The first pair of games were straightforward enough as a 6-1 aggregate win was recorded but it was tougher to see off the Eastern Europeans.
After a narrow 1-0 win in Glasgow, Celtic – who play Partick in the Premiership on Sunday – had to see out a goalless draw on Wednesday to advance by a small margin.
Mackay-Steven is hoping to keep going into the last 32 as he seeks to play in the elite stage of the competition for the first time but doesn’t think it will be easy.
He said: “Obviously it’s a goal of mine this season. In fact now were a tie away it’s very exciting. And hopefully we can make that happen but that will only happen if we play the best we can.
“Having spoken to a few of the boys, we know they (Malmo) are a great team. They won the league last year and any team at this stage in the competition is going to be good.
“We didn’t know too much about Qarabag beforehand but they were a very strong side so I’m sure Malmo will be just as good if not stronger.”
The former Dundee United schemer scored at Firhiill on his Celtic debut last season and he is looking forward to return to the West End of Glasgow after the midweek European exertions.
He said: “I think we are always confident going into every game. But Partick Thistle like to get the ball down and play and pass it. And they’re a good team and they’ve added a few players this year too so it will be a little bit different from last year.
“But hopefully we can go and get the win on Sunday. It was my first game here so definitely it’s somewhere that I’m looking forward to going back to on Sunday.
“I think being here you’ve got the best facilities and team in place to leave no stone unturned. Thursday we had a day off for a rest and today we’ve come in were still doing recovery work so come Sunday we will be ready.”