Bale, 26, has not played since injuring his calf in Real Madrid's 5-1 win against Sporting Gijon on 17 January.
Liverpool expect Allen, 25, to be out "for a while" with a hamstring injury.
Wales assistant manager Osian Roberts is "hopeful" Bale will be fit but said: "The most important thing is the injury clears up because it can re-occur."
Bale is expected to miss Real's Champions League game against Roma on Wednesday after suffering a minor setback in his recovery.
"Time will tell over the next two or three weeks how that develops as Gareth steps up his rehab, and we'll take it from there," added Roberts.
"He's got some key games coming up for Real Madrid and it's important for us that he's fully fit for such an important tournament in the summer.
"Both ourselves and his club will have Gareth's best interests at heart. It's important that the injury fully heals and he doesn't come back too early."
Wales host Northern Ireland at Cardiff City Stadium on Thursday 24 March before facing Ukraine in Kiev four days later as part of their preparations for Euro 2016.
Allen is likely to miss Liverpool's League Cup final against Manchester City on Sunday 28 February after his penalty against Stoke in the semi-final shootout secured their place at Wembley.
"Joe has been unlucky with injuries. As far as the friendlies are concerned it's going to be tight. Time will tell," said Roberts.
"There's no need to rush him back. We know what Joe can do.
"The important thing is that the injury is fully healed and he can have a run of games before the end of the season."
Roberts was speaking at a Football Association of Wales grassroots coaching conference at Dragon Park in Newport.
Wales are unsure if forward Gareth Bale and midfielder Joe Allen will be fit for their friendly matches against Northern Ireland and Ukraine in March.