Laidlaw, who has been capped for Scotland at scrum-half, will form a half-back partnership with Mike Blair from the start at Murrayfield, having been effective moving to the position earlier in the tournament - most notably in the stunning 48-47 win over Racing Metro last month.
Edinburgh are three points behind the Blues and seeking to bounce back from their 25-8 loss in Cardiff last Friday.
Should they win and deny their opponents a losing bonus point, Michael Bradley's side will take the lead in the pool with two rounds of fixtures remaining in January.
The selection of Blair alongside Laidlaw, who is likely to start opposite Cardiff's Scotland fly-half Dan Parks, is the only change in the backline, with Harry Leonard making way.
Laidlaw is also set to continue kicking duties with full-back Chris Paterson's groin problem limiting his practice.
In the forwards, Grant Gilchrist and Netani Talei come in for Esteban Lozada and Stuart McInally in the second and back rows, respectively.
McInally is omitted from the matchday 23, with openside flanker Ross Rennie preferred on the bench.
Fijian Talei told www.edinburghrugby.org: "Everyone's looking forward to this game. The boys are confident and have been focused on this match since we left Cardiff on Saturday. It's a big, big game for us.
"Cardiff have the ability to slot points from pretty much anywhere within 50 metres so we can't afford to give away cheap penalties.
"We have to tackle the basics first at the ruck and the tackle area - that's what Cardiff are very good at.
"If we put our focus there first and give our backs the go forward we're capable of scoring tries from anywhere around the park."
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