A minute's applause will be held before the second qualifying round second leg for Reilly, who scored 238 goals for Hibs and helped them to three league titles in the early post-war period.
A fuller tribute will be paid to the former Scotland centre-forward, who netted five goals in Wembley clashes with England, when Motherwell visit Leith in the Scottish Premiership opener.
But Easter Road will be an emotional place on Thursday night as Hibs fans gather for the first time since Reilly died aged 84 in the early hours of Monday.
And Fenlon wants his players to rise to the occasion and pay their own homage to Reilly, who led the club's 'Famous Five' forward line, as they bid to overturn a 2-0 deficit against the Swedish league leaders.
The Irishman said: "It's been a very sad and difficult week for everyone associated with the club. He was obviously one of the best players the club has ever had.
"If you're looking for a true Hibs man through and through, he fits the bill.
"I met him a couple of times around the ground on match day. He was a gentleman as well as being a very, very good footballer.
"It would be a nice way to pay real tribute to his memory if we can go and win the game.
"It would be lovely to put a smile back on people's faces.
"We're hoping we can do it justice. We've got a tough task but we are playing at home and we're looking forward to a big crowd getting behind us here.
"If we can nick the first goal, let's see what happens."
Hibs captain James McPake is aiming to take inspiration from the life of Reilly, who scored 22 goals in 38 internationals.
"I had the pleasure of being in his company at a good few events through the club," McPake said.
"The last time I met him was April and even then he was in good form, he was joking away. We had lost to St Johnstone the night before and he was having a bit of a go at me for the way we had played.
"That was Lawrie, he was great to everyone and we were all glad when he was round the place.
"We were all deeply saddened by the news at the start of the week.
"But it's spurring us on a bit because we want to go out and do it for him and his family."
Large queues assembled at Easter Road on Wednesday afternoon as fans added to the 11,000 tickets already sold by lunchtime.
"He was such a legend and such a hero to so many of the people that come here," McPake said.
"The fans will be here paying tribute to Lawrie and that's only going to help us with emotion and the atmosphere.
"It's something we have got to react to and use."
Meanwhile, Fenlon refused to comment on the club's pursuit of Swindon striker James Collins.
Hibs are reportedly in talks with the 22-year-old Irishman, who scored 18 goals last season, after having a bid accepted.
Fenlon, who is missing the injured Ryan McGivern, Tim Clancy and Paul Cairney against Malmo, said: "I'm not going to comment on it. There's enough being said about it outside of the club.
"We'll try and do our business and when we get something done we'll let people know as soon as we can."