Pirates trainer Todd Tomczyk said Wednesday that Taillon will be re-evaluated next week before deciding on the next course of treatment.
Taillon, 25, discovered an abnormality after going on the disabled list May 6. He had tissue surgically removed on May 8.
Taillon, who is 2-1 with a 3.31 ERA in six starts for the Pirates, has been cleared to play catch and do light cardio but remains out indefinitely pending the outcome of further test results.
Also for the Pirates, outfielder Gregory Polanco was placed on the 10-day disabled list because of a hamstring injury.
The move was made retroactive to May 15.
Outfielder Danny Ortiz was recalled from Triple-A Indianapolis to fill the open roster spot.
Information from The Associated Press was used in this report.