Royal Bank of Scotland (RBS) is set to appoint Sir Howard Davies as its new chairman, according to reports.According to the Financial Times - the lender which has been looking for a chairman since last year, when Sir Philip Hampton announced he was leaving for GlaxoSmithKline - could appoint Davies as early as this week, when it announces its full year results.The former head of the now-defunct Financial Services Authority, a role which he covered between 1997 and 2003, Davies is currently chairman of the Airports Commission, which is due to make its recommendations on where to build a new runway after the general election in May.Davies is thought to be unlikely to join the taxpayer-owner lender until after the Airports Commission reports and would be expected to join in the summer, while Hampton will complete his move to GSK on 1 September.On Monday, RBS shares closed up 0.33% to 398.80p.