Sporting visit the Wanda Metropolitano in the first leg of the Europa League quarter-finals on Thursday, with both clubs looking to salvage continental campaigns stunted by Champions League group-stage exits.
Jesus' side finished third in a tough Group D topped by Barcelona, although the use of man-marking tactics proved effective in keeping Messi scoreless over two meetings.
However, the Sporting boss is adamant that approach would prove ineffective against the in-form Griezmann, who has netted 10 goals in his last seven club appearances.
"I think [we will not use the same method] because Messi is very different. He does not change his position as much as Griezmann," Jesus told Marca .
"It's more of a zone and it was easier, so to speak, to organise defending him. His position is more fixed.
"[With Griezmann] we are going to find a player who goes all over the field. We will be very attentive to him, knowing he can make the difference."
Sporting have not been beyond the Europa League's final eight since they reached the semi-finals against Athletic Bilbao in 2011-12.
Atleti went on to win the tournament that season and Jesus views them as the frontrunners to claim the trophy for a second time under Diego Simeone.
"For me they are the clear favourites and have all the potential to win the Europa League," he said.
"But we are a team with many resources and with quality. We can win and pass through the tie, without a doubt."