The 24-year-old endured a low-key first season at Tottenham Hotspur.
The England legend raves about the West Ham man.
The snapshot of Republic of Ireland defiance came in first-half stoppage time and it reinforced the broader picture of their European Championship campaign.
The Everton star is yet to feature for England at Euro 2016.
HITC Sport understands that Boro are hoping to finalise deal for Marten De Roon this week.
Aston Villa are reportedly keen on Watford shot stopper Romelu Lukaku.
The two players secured moves to Ibrox earlier this month.
Walters was a second-half substitute during Ireland's 2-1 defeat to France on Sunday, despite admitting he was not fully fit.
The West Ham United star has been the key man for France at Euro 2016.