The 36-year-old left-handed opening batsman was recently persuaded to end his Test retirement by new chairman of selectors Asantha de Mel and arrived in England ahead of schedule (he is still a one-day regular) during the drawn first Test at Lord's.
Sri Lanka collapsed to 192 all out in the first innings but a much improved performance second-time around saw them bat for 14 hours to save the game.
Neither Sri Lanka coach Tom Moody, the former Australia international, nor captain Mahela Jayawardene were consulted about Jayasuriya's recall and the former skipper was omitted from the ongoing tour match against Sussex, the tourists' last before they go to Edgbaston for the second Test.
But an upbeat Jayasuriya said: "It doesn't rule me out because they are trying out a few players here.
"I'm just practising and getting settled down in England. We don't know about the team - if I'm picked I always love to play for my country, if not I'll have to sit out the game.
"I have no problem with the players or coach so returning was nothing serious," he added.
But with the second and third Tests, the latter at Trent Bridge, back-to-back, Jayasuriya knows he cannot take a recall for granted after the team's battling display at Lord's.
"It was a good fightback from the whole team," Jayasuriya said. "Coming back to draw was really hard work. The boys deserved that, they played very good cricket in the second innings."
However, Jayasuriya was wary of the threat posed by Stephen Harmison.
The Durham fast bowler has been sidelined from Test cricket with a shin injury sustained before the second Test against India in Mumbai two months ago.
But England's spearhead recently returned to first-class action and he will be under consideration by the selectors, who are due to announce their second Test squad on Sunday.
"Harmison is the key guy, the wicket-taking bowler," Jayasuriya also told Sky Sports. "It will be a plus for England if he returns.
"We'll have to play on what we'll see from him, it will be tough for us. After the Ashes, England have improved a lot."
Jayasuriya has scored 6,613 runs in 102 Tests with 14 centuries. He is also the fourth batsman to have scored 10,000 runs in one-day internationals after India's Sachin Tendulkar and Sourav Ganguly, and Pakistan's Inzamam-ul-Haq.