The Colombian international joined the Red Devils on a season-long loan deal from AS Monaco in the summer, with the Manchester outfit having the option to sign him permanently at the end of the 2014-15 campaign.
Falcao's arrival at Old Trafford was met by a wave of optimism as supporters looked forward to a potential destructive attacking trio of Robin van Persie, Wayne Rooney and Falcao.
The former Atletico Madrid favourite, however, has yet to hit top form this season and has often found himself watching on from the substitutes’ bench.
With question marks remaining over a long-term knee injury sustained last season, Falcao’s lack of form currently makes him an unattractive proposition for BBC pundit Lawrenson.
"I don't think Manchester United should sign Radamel Falcao permanently, and I don't think they will,” he told BBC Sport. “He is expensive but that is okay if he is putting pressure on someone like Robin van Persie - the problem is, he isn't.”
“Falcao looks like he is still carrying an injury and he does not look the same explosive player he was before he damaged his knee. I would be saying 'thanks, but no thanks' to his agent."
Falcao has started seven Premier League matches this season, scoring three goals and providing three assists in the process.
After disappointing for an hour during the 2-0 win at Yeovil Town in the FA Cup, boss Louis van Gaal decided to drop altogether him from the matchday squad for the ensuing encounter with Southampton in the Premier League.