Carew, 33, has been without a club since helping England's West Ham United to return to the Premier League last May.
Inter, fifth in Serie A, are short of attacking options after Diego Milito suffered a serious knee injury two weeks ago and were considering offering Carew the chance of a comeback for the rest of the season.
However, Inter were not convinced that Carew would be able to return to Serie A action after medical tests, Gazzetta dello Sport and Corriere dello Sport both reported on their websites.
There was no immediate comment from the club on Wednesday.
Coach Andrea Stramaccioni had confirmed on Tuesday that Inter would offer a trial to the much-travelled Carew, who played for Roma in Italy in 2003-04.