A number of teams are monitoring the situation of Wales Under-21 international Lawrence following a string of top displays at Carlisle United.
Carlisle are hopeful of extending the 19-year-old's time at the club, with his current loan deal set to expire, but a host of clubs are known to be keen on taking him.
Lawrence is out of contract at Old Trafford at the end of the season and this has also come to the attention of some rival Premier League clubs.
Welsh duo Swansea City and Cardiff City are amongst those believed to have been impressed with Lawrence, who could move on in the summer for minor compensation as he is under 21.
However, although United are yet to make an offer to extend Lawrence's current deal, Sky sources have confirmed he could yet be offered a new long-term deal by the Red Devils on the back of his impressive stint in Cumbria.
Earlier this week Lawrence said: "When this loan stay ends it would be nice to stay, but I'll speak to all kinds of different people to see what is the best option.
"I haven't thought about it too much as I've just been concentrating on games. I've really settled in as they are a good group of lads, and I'm enjoying it.
"Getting experience at Carlisle is my main objective, getting games and getting used to the Football League. I want to play as many games as I can while I'm here.
"Manchester United said it would be great experience for me coming here and it has been a bonus getting a chance to play."