Wolverhampton Council is carrying out the work so the pool can be ready for use, soon after Government Covid restrictions were lifted.
Signage has been installed asking people not to enter the pool until the necessary tests have been completed – including samples being sent to laboratories to be checked for water safety and quality.
The pool is expected to open on Monday, August 2, if the results show that it is safe to do so.
Councillor Steve Evans, the council's cabinet member for city environment, said: "We understand that the school holidays have begun for many children and the hot weather has meant people are naturally looking for ways to cool down, but paddling in Tettenhall Pool when water safety checks have not been done is foolhardy.
"It’s important that tests are carried out and we know the results before it’s safe for people to use.
“There are lots of signs around the pool telling people not to enter which are being ignored, as adults and children have been seen playing in the water even though the pool is not officially open.
"Once the pool has passed all the necessary safety tests it will be open."
He added: "We understand that children and youngsters are excited and want to have fun over the summer holidays, which is why the council has plenty of other activities across the whole city to keep them occupied over the summer.”