Three points at the KC Stadium will take the Blues ahead of second-placed Manchester City who travel to Newcastle 24 hours later, while current leaders Arsenal visit struggling Aston Villa on Monday.
So Chelsea’s time, if any, at the summit may be brief but victory on Humberside would maintain a pleasing run.
Last weekend’s FA Cup win at Derby County marked a fourth successive success for a side who’ve conceded just one goal in their last five outings.
And while Mourinho continues to have concerns about the lack of goals from his forwards, the contribution from midfield has masked the deficiencies up front.
The Portuguese manager has claimed the club will not bring in a new striker during the January transfer window to supplement his current trio of Samuel Eto’o, Fernando Torres and Demba Ba.
But with Ba’s Chelsea future looking increasingly uncertain — his last appearance came in the League Cup quarter-final defeat by Sunderland — the Senegal forward’s departure would almost certainly trigger a move for a replacement.
Atletico Madrid’s Diego Costa is one of the high-profile names linked to have been linked with a move to Chelsea.
Meanwhile, Costa’s current team-mate Thibaut Courtois has again questioned his Chelsea future.
The young goalkeeper is midway his third season-long loan at the Spanish club where his performances have drawn widespread praise, prompting Mourinho to describe the Belgian as the best young keeper in the world.
But Mourinho has also spoken of his current number one Petr Cech as the best in the business. And that has prompted growing frustration on the part of Courtois, who has made it clear he now wants his long term future resolved.
“About my future, I cannot wait much longer.I need to make a decision with Chelsea as soon as possible, in March, but at the moment I do not really want to talk because there are so many games and you must be focused,” he said.
Mourinho began his second spell as Chelsea manager with an opening-day 2-0 victory over Steve Bruce’s Hull side at Stamford Bridge.
But City defender Curtis Davies said the Tigers feared no one at the KC Stadium.
Hull have the sixth-best home record in the Premier League, winning half of their 10 games, including a 3-1 victory over Liverpool in December.
“We’re confident we can beat anyone at the KC,” said Davies. “We know we have to be right on our game and, maybe a side like Chelsea have to be slightly off it.
“We’re not going to kid ourselves that if both of us are at 100 percent, that we’re going to outplay Chelsea and win.
“If we’re at our game and we do the right things in terms of frustrating them, then maybe we can nick a goal and keep a clean sheet to win the game.”
Davies added Hull’s defeat at Stamford Bridge taught them a valuable lesson about the demands of the Premier League.
The promoted Tigers were 2-0 down after 25 minutes but rallied in the second half to limit the damage.
“It was a lot of the players’ first game in the Premier League, it was on TV and with Mourinho going back, there was a lot of hype away from the football side of the game,” Davies explained.
“The fact that we managed to come through that 2-0 and make a fist of it in the second half, we grew in confidence.
“We knew it wasn’t going to come much harder than that, so it was a blessing in disguise.”
Chelsea’s Branislav Ivanovic and Frank Lampard are again sidelined while Hull’s Paul McShane is expected to be out for a month with an ankle injury.