It’s believed that a verbal agreement is in place to secure the move, with the Blues now looking to agree personal terms and finalise the agreement to bring the 26-year-old to Portman Road.
Fellow Premier League outfit Hull City felt that they were close to signing Florentino on loan this summer, but their move collapsed when Town came in with a permanent offer.
The 12-cap Portugal Under-21 international, who was born in Angola, came through the ranks at Benfica, spending time on loan at AS Monaco and Getafe before his switch to Turf Moor last summer.
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While his time at Burnley was also a loan at first, it became permanent for a reported fee of €24m (around £20.6m) due to an obligation at the end of last season.
Should Florentino join Town, he will become the club’s seventh new summer signing. It would take their total spend, including add-ons, to just under £100m.
Ipswich boss Gary O’Neil is keen to bolster his midfield options, with Azor Matusiwa (muscle) and Jack Taylor (knee) in a race to be fit to face Sunderland after undergoing post-season surgery.
Fulham’s Sasa Lukic remains a target, while Bayer Leverkusen’s Exequiel Palacios has also been linked. The Blues are also confident that they can agree a deal to re-sign Julio Enciso, who is keen on making the move from Ligue 1 side Strasbourg.