Antonio Conte has just two senior strikers in his first-team squad – Diego Costa and Michy Batshuayi.
The Belgian was expected to start against Bournemouth on Boxing Day with Costa suspended but had to wait until the 94th minute to get on the pitch.
“Belgium striker Michy Batshuayi joined for £33m in the summer but is obviously not ready as far as Conte is concerned”
Conte has £60m burning a hole in his pocket following the sale of Oscar to Shanghai SIPG.
Lawrenson does not expect the Chelsea boss to make a signing but believes he could be tempted to land a veteran striker.
He told the BBC: “Belgium striker Michy Batshuayi joined for £33m in the summer but is obviously not ready as far as Conte is concerned.
“Whether the Italian thinks the 23-year-old will be ready soon is unclear, but the fact he left him out when Diego Costa was suspended against Bournemouth said a lot.
“Up front is the only area where Chelsea look a bit short.
“I don’t think they will sign anyone, but if they do it might be similar to when Manchester United signed Henrik Larsson at the age of 35 during the 2006-07 season.
“By that I mean an experienced striker who would get them goals in the short-term. I don’t know who the 2017 version of Larsson would be, or whether they could get him, but that is the type of player they might be after.
“I don’t see any other weaknesses in their squad.”