The duo were the catalyst for the Foxes' shock Premier League title success last season, contributing 41 goals between them, while Mahrez recorded 11 assists, mostly for top scorer Vardy.
Ranieri had hoped the pair would pick up where they left off this term but there appears to have been a breakdown in the partnership, with Mahrez completing just 10 passes to Vardy all season.
The England international's goals have dried up as a result and Saturday's 2-2 draw with Middlesbrough was the 15th match in a row in which Vardy had failed to score for Leicester.
The pair's struggles have contributed to Leicester sliding down the table and Ranieri says he is desperately searching for a solution.
"Now it's more difficult, everyone is watching Vardy, everyone is double or triple on Mahrez and we have to find a solution," Ranieri told the Leicester Mercury.
"In the Champions League we find the solution but in the Premier League we haven't.
"Of course, it is different because when Mahrez takes the ball there are a minimum of two opponents close to him and if he keeps possession the third arrives.
"We try to do our new tactics but it is not easy to make that immediately We continue with our line, of course, change something."