Chelsea are now level with Arsenal on 25 points from 13 games, nine points adrift of leaders Liverpool.
Senegal international Jackson has taken his time to settle since joining Chelsea last season but both he and Palmer have scored eight league goals already in the current campaign.
"Me and Nico work well together," Palmer told the club website. "We speak to each other every day and we message each other after games. We are trying to work on our relationship to help us on the pitch and hopefully that work is showing."
Chelsea finished sixth last season but have been far more consistent in the league this term having lost only to Manchester City and Liverpool, and Palmer believes they can target a Champions League place.
"It’s too early (to predict this season)," said Palmer. "If we keep winning then we will be near the top four.
"But like the gaffer said Manchester City, Liverpool and Arsenal have been together for more than five years, whereas we’ve only been together for a season. We just want to keep going and winning the games."
Enzo Maresca's side visit Southampton in midweek before travelling to face Tottenham Hotspur on Sunday.