Centre-back Hutchinson, a regular in Birmingham's reserve team, spent a three-day spell at the Pirates' Cribbs Causeway training ground.
"We've had Graham in for training," Ward told the Bristol Evening Post. "He's out of contract in the summer and Birmingham have been good enough to let us have a look at him."
Meanwhile, Yate Town striker Scott Wilson will train with the League Two side again this week after impressing last week.
The former Bristol City trainee has scored 27 times this season and Ward admits it is vital they keep their eye on the non-league game for potential players.
"Scott did well," he said. "We've invited him back this week for another look.
"I didn't become a professional footballer until I was 19, so I fully recognise the fact that players can come in to the professional game a little bit later. A lot of players have the raw tools, and, if they are prepared to work hard, they can achieve."