Gibbs, who has less than six months left on his contract with West Brom, was heavily linked with a move away from the Hawthorns in the winter transfer window.
Though the defender started each of their four games leading up to deadline day, the Baggies were open to letting the former Arsenal man go and also received an offer from Major League Soccer side Inter Miami.
However, the transfer did not go through after financial terms could not be agreed between the parties involved, with the deal deemed not suitable by both West Brom and Gibbs.
The 31-year-old ended up staying at the Hawthorns, but the Baggies had already begun the hunt for a potential replacement and considered a move for Chelsea’s Alonso.
The Spain international had fallen down the pecking order at Stamford Bridge following the arrival of Ben Chilwell from Leicester City in the summer.
Alonso was also left out of the Blues squad for 16 Premier League games prior to Frank Lampard’s sacking following an incident that saw the player and manager fall out at West Brom earlier in the season.
With the Spaniard’s future uncertain at Chelsea, he appeared to be a potential target for West Brom.
However, Alonso has made three league appearances and scored a goal for Chelsea since then, with the player making his way back into the team under Thomas Tuchel.