Ramsey, who is currently earning £110,000 a week, could be offered more than £150,000 a week.
Welbeck signed a £70,000-a-week deal when he signed from Manchester United in 2014 but the injury-prone striker's new deal could be worth over £100,000 a week.
With chief transfer negotiator Dick Law recently stepping down, newly appointed Huss Fahmy will handle the contract negotiations.
It is no secret that Alexis Sanchez and Mesut Ozil are entering the final year of their Gunners deals, but Arsene Wenger has insisted the talks are completely unrelated to any summer uncertainty.
‘It’s not connected at all,’ he said. ‘With the amount of transfer levels and the expected amount of contracts the players want, you will have more and more players going into the final year of their contract.
‘You will be in a position where you either extend for money you cannot afford or you go into the final year of their contract.
‘This season there were 107 players in the Premier League who got into the final year of their contract for the first time. The clubs want too much for normal players, because they say if one player is worth £200m, then this player is worth £50m.
‘But everybody knows £50m is too much. So what happens? The club cannot sell and doesn’t extend the contract, so more players go into the final year of their contract.’