The Belgium global scored in Saturday's 4-2 win over Tottenham in the FA Cup semi-final. Costa and Hazard were substituted on in the 60 minute when the game was locked at 2-2.
They have won only two out of eight league games against Chelsea, Manchester City, Manchester United, Liverpool and Arsenal, as well as losing to Liverpool and Chelsea in both domestic cup competitions.
Up front, Hazard should be flanked by Willian, who scored two goals against Tottenham, and Spanish winger Pedro, as they aim to penetrate the Southampton defence with pace and intricate interplay as oppose to lofted crosses into the box.
Check out the official Premier League ticket hub. That lists of managers includes Alex Ferguson, Arsène Wenger, and Carlo Ancelotti, and Conte and Ancelotti would be the only coaches to do this double in their first season as manager with their club.
"Ability wise, there is only one player above him and we all know who he is: Messi".
"Chelsea, they are used to winning trophies".
Spanish striker Costa has endured a hard couple of months, having failed to score for Chelsea since early March, and with a crucial period of fixtures coming up for Conte's side, it is crucial to have everyone in top form.
Chelsea can strengthen their grip on the Premier League title. And maybe they have more experience than us.
At the back, Cahill should return in place of Ake and reform the partnership with Cesar Azpilicueta and David Luiz, flanked by wing backs Marcus Alonso and Victor Moses in a move which has proved a real success this season.
This incredible season did not look like it was going to materialize earlier in the season, as Chelsea did not have that cutting edge and intensity as they do now.
But the Italian does not expect Chelsea's progress to the finish line to be quite as serene with Tottenham only four points behind heading into the final six Premier League matches. Hopefully this is just a blip in what has been a great season so far.
"For the rest of the season, nothing changes", the Spurs boss said.
"They have a great team and a great squad".