Fenlon told the club's website: "It's not a bad draw from a logistical point of view. Our worst case scenario would've been to travel halfway around the world for one of the games."
He added: "Drogheda are a decent side and one that I know very well indeed - I watched them beat Bohemians 3-0 a couple of weeks ago. I also know their manager really well, so from my perspective that would probably be the ideal scenario. But Drogheda have got a really tough tie against Malmo, who are a quality European side with a great pedigree.
"The fact they are Sweden's most successful club tells its own story. Now we've got plenty of opportunities to see both teams a few times and obtain all the relevant info before the second qualifying round takes place in a few weeks' time. If we can play to our best and produce a committed and controlled performance then I believe we've got a decent chance."
Meanwhile, new St Johnstone boss Tommy Wright would like to see his first game in charge of the Perth side take place in his homeland - but admits it is more likely to be hosted by Rosenborg. The Northern Irishman's side were drawn to play either Crusaders or the Norwegian outfit.
Former Saints number two Wright told Press Association Sport: "I was thinking that it would be quite ironic if my first game in charge was against a Northern Irish side. It would be nice to go back if it was Crusaders. But we can't second guess things.
"I certainly know a bit more about Crusaders but Rosenborg are a big side who have been in the Champions League in the past. The good thing about the draw is that no matter what team we get, logistically it won't be a problem."
Derry City will face Trabzonspor, while St Patrick's Athletic will go head-to-head with VMFD Zalgiris, with the winning side then meeting either FK Teteks or FC Pyunik. In terms of Welsh sides, Airbus UK meet FK Ventspils of Latvia in round one, with the winners then playing Jeunesse Esch or TPS Turku in round two.
Prestatyn face SK Liepajas Metalurgs for the right to take on HNK Rijeka and Bala are up against Levadia Tallinn and then, if they beat them, Pandurii Targu Jiu. There are two more teams from Northern Ireland in action - Glentoran meet KR Reykjavik, with Standard Liege awaiting the victors, and Linfield have been paired with IF Fuglafjordur, the winners then facing Xanthi in round two.