Rovers, currently bottom of the table, host Fulham on Saturday, while fellow strugglers Bolton (18th) and Wolves (16th) are at Manchester United and Tottenham respectively.
Sunday then sees 17th-placed QPR travel to high-flying Newcastle before second-bottom Wigan take on current league leaders Manchester City at the DW Stadium on Monday night.
A win could take Blackburn out of the relegation zone if other results go their way and Kean feels there is a "very good chance" Rovers will have their heads above water so long as they seal the three points against the Cottagers.
Having seen his side spring a surprise in recent weeks by drawing 1-1 at Anfield and winning 3-2 at Old Trafford, though, the Scot knows it is risky trying to predict how games will go and insists the focus simply needs to be on the job at Ewood Park.
"We know some of the teams around us have got difficult fixtures this weekend," Kean said.
"We also know there can be upsets, though, because people probably looked at our last two away games (in the league) and thought we weren't going to get anything.
"What you can guarantee is looking after your own results.
"We will go into the Fulham game with lots more people available, a good training week under our belt and we know if we can get a positive result, there is a very good chance that we can climb out of the bottom three with plenty of games to go."
Blackburn are set to have several key players back available for Saturday's game, with goalkeeper Paul Robinson (calf), winger Junior Hoilett and central midfielder David Dunn (both hamstring) all in line to make their returns from injury having been in full training this week.
Captain Christopher Samba - who Kean says is not for sale after the defender was quoted in L'Equipe saying he felt it was "time for a change" - is also fit again after sitting out the FA Cup defeat at Newcastle last weekend due to an ankle knock and tight hamstring.
After the encouraging results on the road, Rovers were brought crashing back down to earth in their last league outing by a 2-1 home defeat to Stoke.
Since then, it has been announced by a Blackburn supporters group that organised protests against the Rovers hierarchy will resume, and a new 24-hour demonstration got under way outside Ewood Park on Friday.
Kean and club owners Venky's have been the target of protests for much of the season, and although organised action was officially postponed for the final two home matches of 2011, losses in those games against West Brom and Bolton saw many fans continue to vent their anger anyway.
Prior to the postponement in December, organisers had suggested that communication between protesters and the club had improved, but they now claim Blackburn have failed to keep promises on that front.
The results against Liverpool and United seemed to have helped ease the situation, and after the Stoke match, Kean praised the Rovers supporters for getting behind their team, even though they had been beaten.
It is something he hopes to see again on Saturday.
Asked about the new protests, Kean said: "As far as that is concerned, I think the directors and the people at the club are in dialogue with the people who are organising these events.
"All I can say is that I thought the fans who were inside the stadium at the last home game were fantastic.
"The atmosphere was good and I spoke to (Stoke manager) Tony Pulis after the game, and he felt as if it was quite intimidating (for the away side).
"I would echo that, and I felt it gave us the platform for the young players to go out and not play with fear when they had the ball.
"We were disappointed with the way we played in the first half of that game, but I thought we got better in the second half and probably deserved something from it, and I felt the fans were excellent. I would really like to witness that again because it really helped us.
"I think the average age of the team that started at Old Trafford was 23 and that it was the youngest Blackburn side ever to play in the Premier League, and I think the team that finished was even younger.
"For young guys who are just starting their career, I think when they can feel the home fans are with them, they can feel that edge against the opposition."
