Gylfi Einarsson was at Ninian Park yesterday. He's due to move to Leeds later in the week as he looks for a UK club.
"The big attraction with him is he's available on a Bosman free transfer," Lawrence told the Western Mail.
"In that sense, he would be a catch. You don't get many 'Bosmans' of that quality knocking about. But there are several clubs interested in him. He's going to Leeds later in the week and I don't know what the player will end up doing.
"We won't be the only club in this division that's interested in him, that's an absolute certainty. There will be competition for his services. I just made it my business to get him here first. It's not a trial, but he's training with us so we can have a look at him and he can have a look at us."
Einarsson has scored 13 goals in 22 games for Lillestrom. He is an attacking midfielder and an Icelandic international. He turned 26 last week.