The Premier League match is the first between the two fierce rivals since the publication last week of an independent report into the Hillsborough disaster which exonerated Liverpool fans from any blame in the 1989 tragedy that claimed 96 lives.
Evra and Suarez were involved in a major controversy last season which resulted in Suarez being banned for eight matches for racially abusing Evra at Anfield last October.
Sunday's occasion is likely to be highly emotional with both Manchester United and Liverpool players and managers urging fans throughout the week to show respect to each other.
Fowler told BBC Radio 5 live it would be appropriate for Suarez and Evra to help defuse the tension by showing unity before kick-off.
"It would be nice for Luis Suarez to put some flowers at the United end regarding Munich, and for Patrice Evra to do so at the Kop," Fowler said.
"The two clubs do have a rivalry, but some things are far more important than football and this is one of them."
Fowler suggested Suarez should commemorate the Munich air disaster of 1958, in which eight Manchester United players and three club staff were among 23 people killed, while Evra should pay tribute to the Hillsborough victims.
Suarez refused to shake Evra's hand before the start of the last game between them in February at Old Trafford.
Tributes have been paid to the 96 at Premier League matches since the report was issued with Liverpool's neighbours Everton staging a particularly poignant one before their match with Newcastle United at Goodison Park on Monday.
JOINT RESPECT
Manchester United defender Nemanja Vidic, who has been sent off twice at Anfield, believes the Goodison spirit should be taken into Sunday's game and in an interview with The Sun newspaper he said: "We have to show an example and be on top of the situation and behave well.
"There is a lot of history with these two clubs. We have had some tragedies, they have as well. I think we should respect each other because we are big clubs and clubs that are respected in the world."
Two United fan groups, the Manchester United Supporters Trust and the Stretford End Flags, have urged fans not to sing disparaging songs about the Hillsborough disaster. Rival supporters have sung distasteful chants about Munich in the past.
Manchester United manager Sir Alex Ferguson said the build-up to the game could affect the players.
"It is a possibility, I don't deny it, human nature can be that way," he told a news conference, hoping the fans behave.
"Liverpool have done their bit and we have done our bit, so let the game go on."
Liverpool go into the match in 17th position and without a league win this term although they beat Young Boys 5-3 in Berne in the Europa League on Thursday.
United have won three of their four league games, are second in the table and beat Galatasaray 1-0 in the Champions League on Wednesday.
