Morata, 25, has missed his side's last four matches due to the problem, with Conte admitting during a press conference last Friday [9 February] the club doctors have still not got the bottom of the issue.
The Blues boss confirmed the Spain international would not be involved against Alan Pardew's side, admitting he still wasn't sure when his player will be available again.
Over the weekend, Morata's wife Alive Campello posted a video of the couple dancing of Instagram which has since been removed after the striker was targeted with criticism by Chelsea fans – with one user replying to the video: "Doesn't look like your back it doing too bad Alvaro."
But replying to a comment on a fan Instagram account, Morata played down the significance of the video, insisting it is an old clip before providing a positive update on his own fitness.
"It's an old video. I'm not injury [sic] I'm okay for the game tomorrow. A lot of critics now... but no problem for me," the former Real Madrid striker wrote on Sunday," the Mirror report.
Chelsea have lost their last two games to Bournemouth and Watford respectively in Morata's absence with Conte suggesting last week that Olivier Giroud could make his full debut against the Baggies on Monday [12 February].
The Italian's assessment of Morata was a rather bleak one, telling reporters he had no idea when his striker will be available again.
"Giroud has trained and will be in contention. We are talking about a lot of bad results, but sometimes we forget we are facing a serious situation," Conte said.
"Players like Morata are very important for us and have been missing for a long time. I don't know how long he will be out. We are struggling to find a solution to solve the pain in his back. If you ask me whether he needs a day, a month or the rest of the season, I don't know. For this season, I am a bit worried. You very well the importance of the player."
Morata was in training over the weekend, however, tweeting a picture of him and teammate Davide Zappacosta leaving the club's facilities in Cobham on Saturday [12 February].