how to convert integer minutes to interval in postgres

you can concat that integer with ' minutes':

t=# with i as (
  select 20::int n
)
select concat(n,' minutes')::interval 
from i;
  concat
----------
 00:20:00
(1 row)

Time: 1.220 ms

Update:

Or: interval '1' minute * n as a_horse_with_no_name says

Fastest way is with make_interval

make_interval(years int DEFAULT 0, months int DEFAULT 0, weeks int DEFAULT 0, days int DEFAULT 0, hours int DEFAULT 0, mins int DEFAULT 0, secs double precision DEFAULT 0.0)

So it looks like this (as suggested by @Teddy)

SELECT make_interval(mins => 20);

or,

SELECT make_interval(0,0,0,0,0,20);

Not to say that's the cleanest, if speed isn't an issue I prefer the * method @a_horse_with_no_name mentioned

SELECT 20 * '1 minute'::interval;