The Cottagers have really hit their stride in recent weeks, winning four on the spin and another victory on Saturday will help them keep pace with Leeds United and West Bromwich Albion in the race for automatic promotion.
Parker has introduced a possession-heavy style of play since taking permanent charge and Fulham's sheer dominance of the ball is evident, especially when you consider that they have had 92 attacks this season featuring more than 10 passes that culminated in a shot or touch in the box - 48 more than any other side in the division.
That style has ensured that Aleksandar Mitrovic gets regular service and the big Serb's brace against Swansea City last weekend took him to 15 for the season.
However, one downside to Fulham's style of play is that they are very susceptible to being hit on the counter, something that has been a strength for City in this campaign.
One key to Bristol City being so effective on the counter has been their use of a 3-5-2 formation, which allows them to work a low block before springing forward with pace in the wide areas.
They did opt for a more traditional 4-4-2 against Huddersfield but given Fulham's approach and home advantage, Johnson is likely to switch to three at the back for Saturday's game.
The Robins have not been particularly consistent this season but they can record back-to-back wins for the first time since August if they triumph at the weekend.
Despite Fulham's impressive form of late, their recent record against City implies that the away side will have more than a good chance on Saturday; Johnson's men have won their last four trips to Craven Cottage in all competitions.
Fulham recent form: DLWWWW
Bristol City recent form (all competitions): DDWDLW
Should none of them be fit enough for a first team return, Parker is likely to field a similar side to that which beat Swansea last time out.
Nathan Baker is also a doubt, having gone off in last weekend's game with a dead leg.
Fulham possible starting lineup:
Rodak; Odoi, Mawson, Ream, Bryan; Johansen, Cairney; Knockaert, Onomah, Cavaleiro; Mitrovic
Bentley; Wright, Williams, Moore; Eliasson, Brownhill, Massengo, Nagy, Rowe; Weimann, Diedhiou.
We say: Fulham 2-1 Bristol City
Although Bristol City have the resources and the nous to take something from this game, Fulham's superior form and home advantage should help them secure a fifth straight league win.
body check tags ::