The goalkeeper has joined Livi on loan from Rangers after being recalled from Queen of the South and will replace Ryan Schofield, who has a thigh problem.
Frontman Kennedy sat out Saturday's Scottish Cup win over Morton, sparking speculation he was left out in case his summer move to Pittodrie was brought forward to January.
But Wright insists it was an ankle knock which kept Kennedy out against Ton and he should be back fit along with Danny Swanson, who has recovered from a bout of illness, to face Livi at the Tony Macaroni Arena.
Livingston provisional squad: McCrorie, Stewart, McMillan, Lamie, Guthrie, Lithgow, Brown, Taylor-Sinclair, Odoffin, Bartley, Lawless, Crawford, Jacobs, Lawson, Sibbald, Pittman, Robinson, Dykes, Erskine, Souda, Tiffoney.
St Johnstone provisional squad: Clark, Duffy, Ralston, Tanser, Vihmann, Gordon, Kerr, Holt, Swanson, Craig, McCann, Wright, O'Halloran, Kane, May, Kennedy, Wotherspoon, Hendry, Booth, Parish.