The Blues opted to step up their transfer pursuit of the forward by submitting an offer for him but were unsuccessful with this particular approach.
Hirst initially emerged as a target for Ipswich in May and is currently attracting a great deal of interest from fellow League One side Portsmouth who are keen to re-sign him.
Pompey boss Danny Cowley has suggested that the club ought to be doing everything in their power to convince Leicester to part ways with Hirst.
During his loan spell at Fratton Park last season, Hirst delivered a host of encouraging performances.
Ipswich have already managed to bolster their attacking options this summer by securing the services of two players.
Freddie Ladapo joined the Blues on a free transfer whilst Tyreece John-Jules was recently signed on a temporary basis from Arsenal.
Kieran McKenna’s side will be hoping to make a positive start to the new campaign when they face Bolton Wanderers at Portman Road on July 30th.
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Unable to turn to the likes of James Norwood and Macauley Bonne for inspiration next season, it will be intriguing to see whether Ipswich decide to submit another offer for Hirst this summer as the forward did illustrate last season that he is more than capable of delivering the goods in League One.
As well as providing 15 direct goal contributions at this level, the forward won 2.7 aerial duels per game as he averaged a respectable WhoScored match rating of 6.90.
Whereas Hirst is currently being given the chance to impress in pre-season, the Blues may be able to convince Leicester to part ways with him if they up their bid.
Given that Portsmouth are also keen on a move, Ipswich may need to act quickly when it comes to this particular pursuit.