The paper adds that the 23-year-old will put pen to paper on a five-year deal worth in excess of £100,000-per-week, double what he is currently earning.
That will make him the club's second highest earner behind record summer buy Mesut Ozil, a reflection on his growing status in north London.
Ramsey joined Arsenal from Cardiff in 2008 in a deal worth £5 million, and after an uncertain start has come into his own this season.
The Welsh international has scored eight goals in 18 Premier League appearances for the Gunners this term - more than he managed in his first five seasons with the club - before injury halted his progress.
Ramsey has been out of action since Arsenal's 3-1 win over West Ham on Boxing Day with a thigh complaint, but is said to be targeting a return against rivals Tottenham on March 16 having resumed training.
The Guardian report that talks between Ramsey's agent and Arsenal have been ongoing for the last month, and that an announcement should be made in the next 48 hours.
Earlier on today, Arsenal announced that both Per Mertesacker and Tomas Rosicky had signed new contracts with the club.
Uncertainty still surrounds the future of Bacary Sagna however - the full-back is out of contract in the summer and is yet to agree terms with Arsenal over a new deal.
Previous reports have suggested that the French international is holding out for the offer of a three-year contract, while so far Arsenal have only been willing to offer a two-year deal.
It has been suggested that Arsenal had planned to announce Sagna's new deal alongside Mertesacker and Rosicky, which could mean that his future lies away from the Emirates Stadium.
Arsenal currently sit four points off Premier League leaders Chelsea following their 1-0 defeat at Stoke on Saturday, and take on Everton in the FA Cup quarter-finals this weekend.