Lawrence was released from Swansea City with his contract due up at the end of the month and the Trinidad and Tobago International will seriously consider a move to the Railwaymen as the player lives not far up the road in Wrexham.
Lawrence who put in some sold displays for the Alex during his loan spell at the club also netted to goal with his last coming in the 4-3 defeat at Stockport County.
Lawrence told BBC Radio Stoke 'I'll sit down and speak to lots of people to decide what happens next.
"I've proven to myself that I've still got a lot to offer. I'll go away and look at what happens for next season."
'It's a massive disappointment, but it's one that we've got to live with because it's a reality," the Trinidad & Tobago international added."Everyone has to push on for next season. This is a massive club and it deserves to be in League One, pushing for the Championship.
"The season has just been not good enough. You can't fault our effort, but trying sometimes is not good enough.
"Now you're going to see what the real men are made of, and we have to make sure we are ready to come back from it."