You can't do that. Uplevel runs the code in a different environment (usually). What you might try is upvar:
set var "test"
proc my_proc {myVar} {
upvar $myVar myLocalVar
puts "myVar is '$myVar' value is '$myLocalVar'"
}
set var "test"
# pass in name of var, not value of var:
my_proc "var"
# should output "myVar is 'var' value is 'test'"