After starting the 2014-15 league campaign with just one defeat from their opening nine outings, Filippo Inzaghi's men have hit a patch of indifferent form in recent weeks.
Their last six outings have seen two wins, two draws and two defeats as they have struggled to find top form.
There were encouraging signs last time out, as goals from Jeremy Menez and Giacomo Bonaventura secured a 2-0 home win over Napoli, a result which lifted them to sixth in the table, two points shy of third place and the UEFA Champions League qualifying berths.
And Mexes, who moved to Milan from Roma in 2011, hopes they can follow up that success with another three points at the Stadio Olimpico.
"Hopefully we can win at Roma," he told the club's official website. "We have not achieved anything yet but the road ahead is still very long.
"We certainly have what it takes in this side to obtain a run of results and become a more consistent team. We will prepare throughout the week for this match.
"We can look back at the match at Genoa which was a tough defeat to take because we felt it was a match we should not have lost. It was important for us to bounce back at home against Napoli, for ourselves and also for the fans.
"Napoli are a side that are battling for third place too so it was a good sign for us when we won. We have to keep going like this and we will head to Rome with the right desire to get a positive result."
The home side could be without head coach Rudi Garcia on the sidelines, after he was handed a two-match ban for an altercation with a steward during the 1-0 win at Genoa on Sunday.
Garcia has vowed to fight the suspension, although the disciplinary proceedings will come as an unwelcome distraction to a Roma side who could be four points behind Juventus when the game kicks off, with the leaders travelling to Cagliari two days earlier.
The capital club have been in strong form in recent times, with 13 points from their last five outings, although they will be without defender Jose Holebas, who is serving a one-match suspension for directing a "provocative and insulting" gesture in the direction of Geona fans at the weekend.
Milan have concerns over defender Adil Rami (thigh), while Marco van Ginkel (ankle), Mattia de Sciglio (foot) and Ignazio Abate (Achilles) are not thought as likely to feature at the Stadio Olimpico.
