The main target on his radar are experienced forwards with former Scotland captain White, who will end his three-year stay with French side Clermont this summer, seemingly the name on most fans' lips.
Lineen hasn't actually spoke to the former Warriors forward but is adamant White fits the profile of what he is looking for and is refusing to rule out making a move to secure his services.
"There are a number of areas that we're looking at, and we've got a few chats going on about various players - it is full-on at the moment," Lineen told the Scotsman.
"Jason is a fantastic player and has been brilliant for Scotland. He will be 34, but you look at the quality and experience he has from being in France.
"He's tough, he's a leader, he's Scottish, he's a good lad and he's been at Glasgow before. You've got to get the balance right.
"The one thing I think we've done well at Glasgow is promote youngsters, with Rob Harley, Ryan Wilson and Stuart Hogg the latest one coming through.
"That's a massively important part of my job but you also look at the wider picture and recognise that it's not just the coaches that help young players develop, but the players around them too.
"You need experienced players on the training paddock, in the analysis, and helping players get into good habits off the field. We haven't spoken to Jason yet but never say never."
63x46.png){kind=logo}