The Academy graduate starred in a 5-2 win away at Crewe Alexandra on his Dale debut, before playing another 90 minutes in a 1-1 draw with Bristol City at his new side’s Spotland home.
Conrad's initial recruitment comes after Dale goalkeeper Josh Lillis sustained an injury in the Greater Manchester club's 2-1 defeat to Chesterfield earlier this month, with Logan being thrown straight into the action in his absence.
One of the Foxes' longest-serving players, Logan has spent 11 years as a professional at King Power Stadium, during which he has enjoyed successful loan spells with Stockport County, Luton Town, Bristol Rovers and Rotherham United.
Next up for newly-promoted Rochdale is a home clash against Bradford City before a JP Trophy trip to Crewe in early September.