Nolasco has been on the 15-day disabled list since June 4 with an impingement in his right ankle. He threw Friday's bullpen session with orthotic inserts, which he had inserted earlier in the week and which pushed back the original bullpen session that was set for Wednesday.
"We can't seem to find the solution to get him coming back in the right direction," Molitor said before Friday's game against the Brewers at Miller Park.
The next step for Nolasco and the Twins is to hear more from the club's training staff before deciding what to do.
The 32-year-old's rehabilitation process has been a turbulent one. He attempted a bullpen session back on June 14, but it was cut short because of discomfort.
If Nolasco is able to get healthy, the club will have decisions to make when it comes to the starting rotation. Ervin Santana is set to make his return to the rotation on July 5 when his 80-game suspension is up.
Nolasco is 5-1 with a 5.51 ERA in seven starts this season for the Twins.
Brandon Curry is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.