Written by Mick Jagger, Keith Richards and Steve Jordan, the song was first written and recorded for possible inclusion on Keith Richards' first solo albumTalk is Cheap. A year or so later Richards played the track for Chris Kimsey and Jagger while recording in Montserrat from March through June for the Steel Wheels sessions. Jordan's writing credit stems from his work with Richards in 1987 and 1988.
Jagger changed some of the lyrics as evidenced in comparison to popular bootlegs of the Richards-Jordan collaboration, but the mood and melody of the song remain in the Rolling Stones track. Charlie Watts adds a thumping bass march to the later song where Richards' sharp, slashing, trademark rhythm guitar is the main percussion on the slightly slower, meandering jam that extended to ten minutes with uncredited piano playing.
Released as the album's third single on January 1990, "Almost Hear You Sigh" made it halfway up the Billboard Hot 100 in the US, going slightly higher in the UK, and number one for one week on the Hot Mainstream Rock Tracks. The fact that the B-side was a Steel Wheels retread, "Break the Spell," and the Rolling Stones comeback 1989 North American tour had finished in December, the song got limited radio airplay. A music video was shot in black and white during the band's 1989 visit to Toronto for two shows at the Skydome.
USA Today music critic Edna Gundersen noted that Jagger's vocals and Richards' guitar playing sounded best on slower Steel Wheels tracks such as "Almost Hear You Sigh." SF Weekly marks it as one of the Stones' best ballads recorded after 1971. However, Parry Gettelman of the Orlando Sentinel marked the track's Grammy nomination as that of a relatively uninspiring song.
The song has been performed rarely since its release, being featured only on the Urban Jungle Tour leg of the Steel Wheels/Urban Jungle Tour.