The Serbia international, 25, only joined Inter from Stuttgart in January but looks set to move on this summer, and the Hammers are reportedly hoping to snap him up for around £5million.
Speaking after Saturday's 2-0 friendly win at Bournemouth, Allardyce said Kuzmanovic was on his radar but stopped short of admitting any bid.
Allardyce said: "He is a player I like, but I know nothing about it so cannot comment."
Goals from Kevin Nolan and Jack Collison gave the visitors victory at Dean Court, and afterwards Allardyce said he was happy with his squad strength at this point - but would still like to bolster his attack.
"For the first time in eight years, I have got a good squad together right at the start of pre-season," he added.
"Normally I am six or seven short and I have to skimp around to get them in, but not this year.
"We would like to add to that of course, although it will only be one or two max. Position wise, we need an attacking player first and then we will see where we go.
"At this moment, it depends on the player who is available. It needs to be a quality player who brings a lot to the team for us to go after him."
Nolan was forced to limp off shortly after the interval but Allardyce insisted there were no serious worries over his skipper.
"Kevin came off with only a dead leg so it looks like he will be OK and it won't be too much of a problem," he told the Sunday Mirror.