Gerrard, 36, is leaving MLS club LA Galaxy and claims he is considering "options on and off the pitch".
Lawrenson feels Gerrard could "definitely play in this Liverpool team" and be used in a coaching role.
"They will not have to pay him fortunes - they can tell him if they need him he'll play," said Lawrenson.
"The most important thing in all this, though, is that he would not be seen as a threat by Jurgen Klopp if he was on the coaching staff.
"He would be brilliant to have around the club because he would be in awe of Klopp, so that is just not a worry. I am sure Klopp would love it too - the only effects would be positive.
"He has already coached Liverpool's under-16 team for a while in 2015 and really enjoyed it," added Lawrenson, who made 356 appearances for the club. "If you are an under-16 and getting coached by Stevie G, then how good is that?"
Gerrard is pursuing his Uefa A coaching licence - the second-highest qualification offered - and has punditry commitments lined up. But Lawrenson believes Gerrard would "definitely be open" to being registered as a player.
He left Anfield in 2015 after spending 17 years in the first team, making 710 appearances, scoring 186 goals and winning eight major trophies.
The midfielder played 34 times for Galaxy over two seasons and insists he will be back in football in some capacity. He has been linked with moves to Celtic and Newcastle in recent weeks.
Klopp allowed Gerrard to train with the first team during the MLS off season and has previously said the former Reds' captain is "always so welcome" at the club.
Lawrenson also wants the club to utilise Jamie Carragher, who retired in 2013 after 737 Liverpool appearances, insisting drawing on the experience of two former greats is "a no brainer".
He added: "I would let those two come in and take a couple of training sessions at Anfield as well. They would offer a different voice and a different point of view, without undermining the manager. Can you imagine them in the coaches room with Klopp? It would be great."

Midway through the first half Ross Hannah had a chance to put Barrow ahead, but his shot was blocked by Michael Ihiekwe.
Andy Cook's excellent volley from 25 yards out, his 19th league goal of the season for Rovers, broke the deadlock and he almost doubled the advantage just before the break.
Barrow levelled in the 63rd minute when Moussa Diarra attacked the ball from a free-kick that was spilled for Inoh Effiong to tap in moments after coming on.
Six minutes later Akil Wright's interception fed Williams, who stunningly found the top corner from 20 yards.
Match report supplied by the Press Association
Match ends, Barrow 2, Tranmere Rovers 1.
Second Half ends, Barrow 2, Tranmere Rovers 1.
Substitution, Tranmere Rovers. Cole Stockton replaces Jay Harris.
Substitution, Tranmere Rovers. Connor Jennings replaces Adam Mekki.
Jay Harris (Tranmere Rovers) is shown the yellow card.
Substitution, Tranmere Rovers. Andy Mangan replaces Ritchie Sutton.
Goal!  Barrow 2, Tranmere Rovers 1. Jordan Williams (Barrow).
Goal!  Barrow 1, Tranmere Rovers 1. Inih Effiong (Barrow).
Substitution, Barrow. Inih Effiong replaces Ross Hannah.
Substitution, Barrow. Akil Wright replaces Dan Rowe.
Second Half begins Barrow 0, Tranmere Rovers 1.
First Half ends, Barrow 0, Tranmere Rovers 1.
Goal!  Barrow 0, Tranmere Rovers 1. Andy Cook (Tranmere Rovers).
First Half begins.
Lineups are announced and players are warming up.
Liverpool should re-sign Steven Gerrard as a player and coach as the "only effects would be positive", says the club's former defender Mark Lawrenson.
[NEXT_CONCEPT]
Jordan Williams' screamer gave Barrow victory over high-flying Tranmere at Holker Street and moved the hosts two points off the National League play-off places.