Directly embedding a psql SET variable inside another string?

Pg 12

I need to pass a \set variable (in this example named v_ssn) into a LIKE string.  A two-stage process (building v_like from v_ssn, and then using v_like in the LIKE string) works, and is fine when executing an sql script, but not so good  is there any way to directly embed v_ssn in another string?

test=# \set v_ssn 345
test=# \echo :v_ssn
345
test=# \set v_like %:v_ssn%
test=# \echo :v_like
%345%

test=# SELECT * FROM employee WHERE ssn LIKE :'v_like';
    ssn    |   name   |  ssn_int  
-----------+----------+-----------
 123456789 | John Doe | 123456789
(1 row)

As expected, this fails:

postgres=# SELECT * FROM employee WHERE ssn LIKE :'%v_ssn%';
ERROR:  syntax error at or near ":"
LINE 1: SELECT * FROM employee WHERE ssn LIKE :'%v_ssn%';