A deal, reported to be worth £12.5million, for the England right-back is at an advanced stage and he would become the sixth arrival at Anfield.
Clyne, 24, is currently on holiday but he is expected to be signed on a five-year deal on his return.
There appears to have been a determined effort to get signings done early this year with the arrival of Hoffenheim forward Roberto Firmino, Manchester City midfielder James Milner, Burnley striker Danny Ings, Charlton defender Joe Gomez and Bolton goalkeeper Adam Bogdan already done.
The capture of Clyne would virtually complete the business the club set themselves after finishing sixth last month, losing their Champions League status after just one year.
Carragher believes completing so much business even before the players are due back in for pre-season should benefit the Reds.
“I saw Nathaniel Clyne at St Mary’s after a game last season and told him to sign for LFC – he took my advice!” the former centre-back wrote on Kicca.
“I think it’s another good signing for the club to go along with the other business already done.
“The early deals were a couple of squad players (Ings and Bogdan) and also James Milner, who are all an improvement on what’s currently in the squad.
“The last week has seen the signings of Clyne and Firmino, which will improve the team more than the squad and that’s what costs the big money.
“Credit to the club for getting these deals done early as every club wants to do that but few do. Another striker still needed though!” The club are continuing their pursuit on that front with interest in Sevilla’s Columbia centre-forward Carlos Bacca and Venezuela’s Salomon Rondon, who have both been in action at the Copa America.
Reds chief executive Ian Ayre has now returned home from Chile having secured the Firmino deal but the pair remain an option, although Sevilla have warned Bacca will not come cheap with a buy-out clause reported to be £25m.
“I’m no fortune-teller but top strikers in the market there aren’t that many. Bacca has averaged 24.5 goals, 21 goals in his first season at the club and 28 in his second,” Sevilla sporting director Monchi told the club’s website.
“I hope no one pays his buy-out clause (£25m). It’s a risk we take but we can’t do anything about that.
“We gave him a new contract 10 months ago and I believe he and his family are very happy here but I cannot predict the future.” With a sixth signing on the verge of completion it means manager Brendan Rodgers has spent about £50m on strengthening his squad – coincidentally the same amount Liverpool value Raheem Sterling at having recently turned down an offer £10m shy of that from Manchester City.
The club maintain this summer’s outlay – particularly that of £29m on Firmino, who will become their second most expensive signing in their history - is not dependent on the sale of their wantaway England winger.
However, with no likelihood of the 20-year-old extending his contract beyond the current two years remaining and relations with his agent Aidy Ward having deteriorated in the last couple of months it appears increasingly possible.
The Clyne transfer is the fourth between Southampton and the Merseyside club in the last 13 months – taking the total cost of Saints signings to £60m — after last summer’s signing of Dejan Lovren, Rickie Lambert and Adam Lallana.
Of that trio only the latter looked close to fitting in at Anfield with Lambert expected to be moved on in the next few weeks and Lovren fighting for his first-team place.
Clyne is not likely to have the competition his former Saints team-mate faced with Javier Manquillo, due to start the second year of his loan from Atletico Madrid, having struggled to impress and academy graduate Jon Flanagan not going to be fit from a second knee injury until late in the year.
Meanwhile former Reds midfielder Dietmar Hamann believes if the club do eventually sell Sterling to Manchester City in the wake of the capture of Roberto Firmino, it will represent their best piece of business for a long time.
Their record £35million deal to bring Andy Caroll to Anfield in 2011 remains a significant embarrassment but Hamann does not believe the Firmino deal is in that league – especially if they end up selling Sterling to City for close to Liverpool’s valuation of £50m having already turned down a £40m offer.
“I’ve not got a problem with the money Liverpool have paid for Firmino,” the German told the Liverpool Echo. “He’s one of the up and coming stars in Brazil and I think he’s worth it. Look at what other clubs are spending. To attract the best you have to pay big money.
“If Liverpool get £50million for Sterling and invest half that money in Firmino the club will have made their best business in a long time.
“To be honest, he’s the type of player I thought Liverpool wouldn’t be able to get without Champions League football,” added Hamann.
“To get him is a real statement of intent and hopefully there will be two or three more big signings to come.
“Expectations had gone down and I was worried that Liverpool would go into the new season on a low.
“We’ve needed a spark from somewhere and this signing has given supporters the boost they needed.”