MK Dons boss Karl Robinson has handed trials to Jay O'Shea, John Dunleavy, Kerrea Gilbert and Ian McLoughlin.
The quartet featured in Dons' 4-1 friendly win over St Neots on Saturday, with striker O'Shea on the score sheet for Robinson's side.
"We've got a few players we are chasing at the moment," Robinson told BBC Three Counties Radio.
"But if the lads come in and really shine, obviously you're stupid not to take them."
O'Shea, 22, was released by Birmingham City earlier in the summer, after a season which saw him loaned out to Stevenage and Port Vale.
Former Arsenal defender Gilbert has finished a spell with Major League Soccer side Portland Timbers, while 20-year-old defender Dunleavy was let go by Wolves.
Similarly, 19-year-old goalkeeper McLoughlin failed to win a new deal with Ipswich Town, and all four could join the Dons squad for their pre-season trip to Dublin.
"I'm looking for someone to really strike me - Jay and a few others are going to come away with us to Ireland," Robinson added.
"And that gives them more time to show us what they've got.
"Because we're running on a small squad this year we need bodies to come in and help us out.
"We help them out because we give them training, it gives other clubs a chance to have a look at them, but I was happy with them."